The structural stability and mechanical integrity are key elements for the proper functioning and preservation of complex living systems. Being in constant interaction with their surroundings and subjected to external inputs, such systems need to be able to face changes in order to thrive. These inputs can affect the system both in a localized way or disturb it as a whole. Any perturbations that cannot be mechanically withstand by the living system will result in a crucial malfunctioning or, ultimately, in its death. The general mechanism responsible for maintaining the system's physiological conditions at the proper state, despite environmental variations, is

Looking back after three years of being a PhD student I can safely and happily say that they were three amazingly and properly spent years. To begin with, I would like to thank Martial, my supervisor, for welcoming me to his research group. Somehow, and I am very grateful for it, he knew I had to be part of his team even before I had any idea about what to do with my future. His complete trust in me and both his life philosophies and great heart made for a stupendous mentor both inside and outside the office. Thank you Martial for all the knowledge shared, the discussions and for being an awesome person. During the project I realized how important the working environment is and how fortunate I was with the group I had joined. Elisa, Katha and Vanni were, hands down, the best office crew I could have asked for. Huge thanks to those three who became great friends aside from helpful and supportive colleagues. Sorry for all the singing though. From random and fun lunch conversations to heated scientific discussions, MOTIV team proved to be a truly awesome and encouraging group. I would like to thank you all, and namely Philippe and Irene for your enormous help and contagious happiness, and Thomas and Aurelian for conversations of every sort.

Inside the lab it was fun, but outside was even better. I want to thank my awesome group of friends without whom this period would not have been the same. Those friends that are the very definition of feeling at home, the feeling of belonging. Friends that I will not get rid of, in the good sense of the phrase, if there is one. Those in the group that were here from the beginning, making my PhD choice easier, as well as those I made along the way and who enriched my life so much more. Thank you so much, and again, sorry for all the singing though.

To my parents, the ones mainly responsible for me being here since they made me who I am, I will keep thanking them every day. Next in line my three best allies, my sisters, and my whole family, my most valuable 'possession'. An endless source of love, support and joy, they are my true north.

To those friends back in Argentina that understood and grudgingly accepted my restless desire for travelling (also applies to my family). Friends that after all these years are still 'by my side' through emails, messages and video calls as if no time had passed wielding at the same time that yet unanswered question: when will you be back? Last but almost ahead of all the rest, I would like to thank one particular friend, Martina, whose personal decision opened for me the doors to this amazing three-year adventure. identified as homeostasis. More specifically, one of the processes known in mechanobiology to preserve the appropriate mechanical equilibrium of a living system is called tensional homeostasis.

It is important to note that all of the above stated holds true both at the scale of collective behaviour of complex organisms, and all the way down to the single cell level. In fact, it is actually this last small scale which draws our interest. Cells face constant mechanical perturbations from their surrounding and are able to respond accordingly maintaining a relatively stable internal mechanical state. The existence of this internal tensional equilibrium relies on a very dynamic process with constant feedback loops between the internal biochemical contractile machinery and the external active generated forces.

Our interest is to understand better this active mechanism by dynamically perturbing the tensional homeostatic system while studying its return to equilibrium.

Mechanical integrity

As a general term, mechanical integrity can be defined as the condition of a system where its parts are properly arranged and in optimum conditions, in order to ensure both the correct functioning of such system and the prevention of any possible failure that might affect it [START_REF] Williams | KBC Advanced Technologies[END_REF]. In nature, this condition can be seen at every level of hierarchy. From the collective behaviour of independent organisms, as is the case of fire ants, through organs and tissues, all the way down to the cell.

Over the last few decades, the emerging field of mechanobiology has identified the cell not only as a widely known complex biochemical sensor, first described as such by Pfeffer in 1884, but also as a sophisticated biomechanical structure were mechanical signals, both internal and external, affect the cellular decision-making in complex environments. Physical environmental and intracellular factors significantly influence vital cellular processes such as migration, differentiation and fate [START_REF] Lo | Cell movement is guided by the rigidity of the substrate[END_REF]- [START_REF] Iskratsch | Appreciating force and shape-the rise of mechanotransduction in cell biology[END_REF].

It is essential for the cell, and the tissue of which it is part, to ensure mechanical integrity, sustaining optimum tensional values and mechanical equilibrium. Collapse of this integrity and abnormal interpretation of mechanical cues may lead to physiological dysfunctions or pathologies such as fibrosis, atherosclerosis and even cancer [START_REF] Dufort | Balancing forces: Architectural control of mechanotransduction[END_REF], [START_REF] Jaalouk | Mechanotransduction gone awry[END_REF]. A dysregulation of cell and tissue forces can disturb the mechanical integrity of the system and its mechanotransduction, thus promoting disease progression [START_REF] Wyatt | A question of time: Tissue adaptation to mechanical forces[END_REF]- [START_REF] Barnes | Tissue mechanics regulate brain development, homeostasis and disease[END_REF].

Among the mechanisms used by the cell to preserve this mechanical integrity, one of the most important, and the one we will be focused on henceforth, is what is known as tensional homeostasis.

Tensional homeostasis

The concept of homeostasis

The process of cellular tensional homeostasis started to be defined after the work done by Brown and colleagues in 1998. However, the general mechanism of homeostasis has been around since the 19 th century and I would like to spare a few lines to bring this concept into context, before diving into the more specific tensional one.

In 1865, French physiologist Claude Bernard (Fig. 1A left) elaborated the concept of 'milieu interieur' (internal environment), stating that it is the stability of this environment what gives an organism freedom and independence from the external environment.

Quoting one of Bernard's arguments:

"The stability of the internal environment implies an organism so perfect that it can continually compensate for and counterbalance external variations. Consequently, far from the higher animals being indifferent to their surroundings, they are on the contrary in close and intimate relation to them, so that their equilibrium is the result of compensation established as continually and as exactly as if by a very sensitive balance.'' [START_REF] Cooper | From Claude Bernard to Walter Cannon. Emergence of the concept of homeostasis[END_REF]. Garrison. [START_REF] Davies | Adaptive homeostasis[END_REF].

Almost 70 years later, the American physiologist Walter Cannon (Fig. 1A right) reformulated Bernard's idea of the constancy of the milieu interieur by coining the, now widely known, concept of homeostasis (The Wisdom of the Body, 1932). This new term conveyed the idea that biological organisms, being in constant interaction with the outer environment, would be able to maintain and adjust internal conditions within 'narrow limits' when faced with external disturbances. It is important to note that the choice of the word was not arbitrary. Cannon decided to use the prefix "homeo" (Greek meaning 'like' or 'similar') instead of "homo" ('same' or 'fixed'), to transmit the notion that the constancy of this internal physiological state is more relative than absolute [START_REF] Cooper | From Claude Bernard to Walter Cannon. Emergence of the concept of homeostasis[END_REF], [START_REF] Davies | Adaptive homeostasis[END_REF] (Fig. 1B).

Following this same line, Bornstein and colleagues coined the term of dynamic reciprocity in 1982, which was further elaborated by Mina Bissell et al during that same year (Fig. 2). This concept derived from the homeostasis ideas of Cannon but also introduced the notion that cells actively react to the extracellular matrix (ECM) influences, responding accordingly and altering the composition and structure of the ECM, hence creating a feedback loop in between both sides. Bissell's work would emphasize the idea of the important role that the ECM played on the cell's fate by stating that "the influence of ECM on the cell, both during the developmental process and in established tissues, appears to evolve continually." [START_REF] Bissell | How does the extracellular matrix direct gene expression?[END_REF]. This idea of a bidirectional interaction between cells and their microenvironment proved to be right, enhancing the understanding of the cellular homeostasis and expanding the approaches needed to study such a dynamic phenomenon.

Figure 2 A graphic depiction of the principle of Dynamic Reciprocity. The ECM impacts on the cell's functions and behaviour, and the cell responds accordingly modifying the environment. Adapted from [START_REF] Schultz | Dynamic reciprocity in the wound microenvironment[END_REF].

Tensional homeostasis at the single cell level

The term homeostasis has been kept until today and used in many different fields and at different hierarchies. As a consequence, it was in 1998 that Brown et al presented tensional homeostasis as "the control mechanism by which fibroblasts establish a tension within their extracellular collagenous matrix and maintain its level against opposing influences of external loading" [START_REF] Brown | Tensional homeostasis in dermal fibroblasts: Mechanical responses to mechanical loading in threedimensional substrates[END_REF]. Since then, tensional homeostasis has had slightly diverse definitions in the literature but it roughly relates to the ability of cells to maintain or attempt to maintain a constant level of tension when faced with perturbations from the extracellular matrix.

Such control mechanism is of utmost importance for the cellular integrity. Attempts at properly understanding the processes involved in this phenomenon have rapidly increased over the last few years and I will talk about them throughout this chapter. Mechanical interactions between the cell and its environment can be divided into three main categories. A normal loading situation is where forces applied by the ECM are correctly countered by the cell resulting in the maintenance of a physiological tensional state. An overloading, such as an abnormal remodelling of the ECM, can exceed the limits of tensional response of the cell, resulting in a pathological response such as fibrosis. A degradation or loss in the mechanical properties of the ECM can induce the cell into apoptosis. Adapted from [START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF].

Nowadays, it has been well reported that the process of tensional homeostasis is regulated in the cell through mechanotransduction; the cellular machinery senses internal and external mechanical cues and transforms them into biochemical signalling [START_REF] Ciarletta | On residual stresses and homeostasis: An elastic theory of functional adaptation in living matter[END_REF].

Cellular mechanosensing tools

The mechanosensing machinery (Fig. 4) of the cell comprises both intracellular and extracellular ingredients, among which the most important structural ones are the membrane and its cell surface adhesive protein complexes, the nucleus, and the cytoskeleton. The cell surface adhesive protein complexes that mediate the attachment to the surrounding extracellular matrix are known as focal adhesions, and the ones involved in attaching to neighbouring cells are identified as cell-cell junctions. Focal adhesions are macromolecular assemblies consisting of transmembrane proteins, integrins, which mediate the cell interaction with extracellular ligands, and intracellular proteins connected to the actomyosin cytoskeleton [START_REF] Tamkun | Structure of integrin, a glycoprotein involved in the transmembrane linkage between fibronectin and actin[END_REF]- [START_REF] Goldmann | Mechanotransduction and focal adhesions[END_REF]. Cell-cell junctions, on the other hand, consist mainly of Cadherins, transmembrane proteins that form adherent junctions binding cells to each other [START_REF] Leckband | Cadherin Adhesion and Mechanotransduction[END_REF], [START_REF] Dorland | Cell-cell junctional mechanotransduction in endothelial remodeling[END_REF]. On the non-adhesive side of the cell surface there are mechanosensitive ion channels (or stretch-gated ion channels) involved in sensing mechanical forces coming from variations in the flow of fluids, such as blood, or pressure differences, as is the case of sound. They are vital for processes such as touch and hearing, as well as feeling and memory formation [START_REF] Gottlieb | Gating the mechanical channel Piezo1: A comparison between whole-cell and patch recording[END_REF], [START_REF] Delmas | XMechano-gated ion channels in sensory systems[END_REF], and when opened by physical forces and deformation they can induce electrical signals and ion exchange.

Looking at the inner part of the cell, the cell nucleus and the nuclear lamina have been found to possess its own mechanical machinery that can respond to and transduce mechanical stimuli coming both from the cell (through the actomyosin cytoskeleton) and from inside the nucleus (through altered gene expression and transcriptional profiles) [START_REF] Shivashankar | Mechanosignaling to the Cell Nucleus and Gene Regulation[END_REF]- [START_REF] Snedeker | The nuclear envelope as a mechanostat: a central cog in the machinery of cell and tissue regulation?[END_REF].

The cytoskeleton, consisting mainly of actin filaments, microtubules and intermediate filaments, is a network which spans the whole cell body preserving its shape and mechanical integrity. It is connected to each of the previously mentioned components, allowing for force transmission in between cells and in between the cell and the extracellular matrix. This network, in collaboration with motor proteins, such as myosins, modulates crucial cellular processes such as migration [START_REF] Isenberg | Vascular smooth muscle cell durotaxis depends on substrate stiffness gradient strength[END_REF], division [START_REF] Lafaurie-Janvore | ESCRT-III assembly and cytokinetic abscission are induced by tension release in the intercellular bridge[END_REF],

differentiation [START_REF] Engler | Matrix Elasticity Directs Stem Cell Lineage Specification[END_REF] and cell shape [START_REF] Oakes | Geometry regulates traction stresses in adherent cells[END_REF]. By provoking actomyosin contraction it balances intracellular and extracellular forces [START_REF] Dufort | Balancing forces: Architectural control of mechanotransduction[END_REF], [START_REF] Papusheva | Spatial organization of adhesion: force-dependent regulation and function in tissue morphogenesis[END_REF]- [START_REF] Das | A molecular mechanotransduction pathway regulates collective migration of epithelial cells[END_REF]. Moreover, the variations of its length, density, cross-linking and arrangement, together with its kinetics and dynamics, directly regulate cell's mechanical properties such as contractility, rigidity and motility [START_REF] Dufort | Balancing forces: Architectural control of mechanotransduction[END_REF], [START_REF] Murrell | Forcing cells into shape: The mechanics of actomyosin contractility[END_REF], [START_REF] Ennomani | Architecture and Connectivity Govern Actin Network Contractility[END_REF]. Finally, the membrane as a whole has been seen to act as a global tensional sensor which, through the combination of cortical, substrate and membrane tension, regulates cellular processes and parameters such as shape, polarity and motility [START_REF] Gauthier | Mechanical feedback between membrane tension and dynamics[END_REF]. Moreover, recent results suggest that the overall shape of the cellular membrane is a separate signal source which can modulate mechanical signalling and 'store' information coming from both chemical and physical sources [START_REF] Ron | Cell shape information is transduced through tension-independent mechanisms[END_REF].

Figure 4 A representative scheme showing the processes and structures involved in cellular mechanosensing. An initial external mechanical stimulus (such as shear flow, ECM remodelling or cellcell contact) is sensed by the cell surface proteins which trigger a signalling cascade inside the cell. This cascade may lead to a modulation of gene expression at the nucleus that will impact on cell functions such as polarity, migration and fate. Adapted from [42].

Signalling elements, which work in tight interaction with focal adhesion proteins, are the second set of important ingredients that contribute to the cellular tensional homeostasis and mediate cellular force responses and contractility (Fig. 5). Among the main players that can be activated at the onset of a physical stimuli, we found the Rho-family GTPases, such as RhoA, responsible for inducing actin cross-linking and remodelling, protein phosphorylation and ultimately mediating gene expression by affecting the activity of transcriptional factors [START_REF] Dufort | Balancing forces: Architectural control of mechanotransduction[END_REF], [START_REF] Oakes | Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres[END_REF]- [START_REF] Chrzanowska-Wodnicka | Drives the Contractility Formation of Stress Fibers and Focal Adhesions[END_REF]. Another signalling pathway which can be activated through integrin sensing and has been recorded to regulate cell differentiation and proliferation, is the mitogen-activated protein kinaseextracellular signal-regulated kinase (MAPK-ERK) pathway [START_REF] Jaalouk | Mechanotransduction gone awry[END_REF], [START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF], [START_REF] Khatiwala | ECM compliance regulates osteogenesis by influencing MAPK signaling downstream of RhoA and ROCK[END_REF]. Transmembrane receptors known as integrins mediate the external mechanical interaction between the cell and the ECM while at the same time being in direct contact with the internal signalling molecules that also make up the focal adhesion complexes. Upon mechanical stimulation (communicated by the integrins) these signalling molecules will trigger the signalling cascades MAPK and Rho that will lead to gene regulation at the nucleus, and mechanical responses from the actomyosin network, ultimately affecting posterior cellular response and adaptation. Adapted from [START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF].

All the sensing machinery aforementioned safeguards the mechanical integrity of the cell against an environment that subjects it to a variety of exogenous forces such as shear stress, gravity, and compressive and tensile forces [START_REF] Handorf | Tissue stiffness dictates development, homeostasis, and disease progression[END_REF]. The proper understanding of how mechanical signals are assimilated and transduced into biochemical responses is of paramount importance. Dysregulation or malfunction of any of these sensing elements can affect the cell and the whole tissue, leading to apoptosis or progress into pathological conditions. Moore and collaborators have reported that the inhibition of the RhoA pathway affects the developing lungs by preventing branching angiogenesis and epithelial budding [START_REF] Moore | Control of basement membrane remodeling and epithelial branching morphogenesis in embryonic lung by Rho and cytoskeletal tension[END_REF]. Other authors have found that erroneous mechanical response from endothelial cells to turbulent blood flows can lead to a pro-inflammatory state which can develop into atherosclerosis [START_REF] Mehdizadeh | New insights in atherosclerosis: Endothelial shear stress as promoter rather than initiator[END_REF], [START_REF] Nigro | Flow Shear Stress and Atherosclerosis: A Matter of Site Specificity[END_REF]. A higher uncontrolled cytoskeletal tension as a result of abnormal stromal interaction increases the risk of expression of malignant genes leading to tumours [START_REF] Ciarletta | On residual stresses and homeostasis: An elastic theory of functional adaptation in living matter[END_REF], [START_REF] Jain | The Role of Mechanical Forces in Tumor Growth and Therapy[END_REF].

Extracellular matrix contribution to the cell mechanical state

Even though I have focused so far on explaining why it is so important that the cell protects itself against extracellular modifications, we are missing the other half of the story. As it was hinted by the concept of dynamical reciprocity in the opening paragraphs, the cell not only relies on external cues and physical stimuli to thrive and develop (Fig. 6), but it also exerts forces and plays an active role in modifying the mechanical properties of its surrounding. As a matter of fact, tissue rigidity and exogenous and cell-cell forces play an important role on cellular activities [START_REF] Handorf | Tissue stiffness dictates development, homeostasis, and disease progression[END_REF]. Similar to what it was depicted on Figure 3, this condensed graph shows a minimum of cellular apoptosis when the stress that the cell senses is within the homeostatic range, and an increase in cell death outside this range. Adapted from [START_REF] Chan | Mechanostasis in apoptosis and medicine[END_REF].

Indeed, this concept of the cell relying on mechanical stimuli from the environment was also posed by Grinnell in 1994: "As long as the tissue is under mechanical stress, cell proliferation and biosynthetic activity will persist. Once mechanical stress is relieved ... cells will switch to a non-proliferative phenotype and begin to regress even in the continued presence of growth factors.'' [START_REF] Grinnell | Fibroblasts, myofibroblasts, and wound contraction[END_REF].

The role of the ECM in mechanically regulating the cellular behaviour and development has been thoroughly researched in the field of mechanobiology [START_REF] Handorf | Tissue stiffness dictates development, homeostasis, and disease progression[END_REF],

[52], [START_REF] Asnacios | The mechanics behind cell polarity[END_REF]. Kilian et al found that geometric features which increased actomyosin contractility promoted osteogenesis while reduced actomyosin contractility drove the stem cells towards adipocytes [START_REF] Kilian | Geometric cues for directing the differentiation of mesenchymal stem cells[END_REF] (Fig. 7). Geometrical cues have been also shown to control the positioning of branching during morphogenesis of mammary epithelial cells and primary organoids [START_REF] Nelson | Tissue Geometry Determines Sites of Mammary Branching Morphogenesis in Organotypic Cultures[END_REF]. In the case of tissues used to high loading, such as bones and cartilage, it has been reported that reduced mechanical stimulation results in a reduction of proteoglycan content and bone mineral density [START_REF] Handorf | Tissue stiffness dictates development, homeostasis, and disease progression[END_REF]. Moreover, further studies have shown an enhancement in the expression on bone-transcription factors, induced by MAPK/ERK pathways, on stiff matrixes in contrast with softer matrixes [START_REF] Khatiwala | ECM compliance regulates osteogenesis by influencing MAPK signaling downstream of RhoA and ROCK[END_REF]. Bissell and Radisky have even claimed that an effective regulation or 'normalization' of the tumour mechanical environment can help in the prevention of cancer progression [START_REF] Bissell | Putting tumours in context[END_REF]. The rearrangement of the ECM physical properties inflicted by cell forces and protein deposition can also lead to pathologies in case of exacerbated or altered modifications. Fibrotic diseases appear as a consequence of abnormal or elevated ECM deposition by the cell [START_REF] Camand | Long-term changes in the molecular composition of the glial scar and progressive increase of serotoninergic fibre sprouting after hemisection of the mouse spinal cord[END_REF], and increased matrix stiffness as a result of ECM remodelling can play a crucial role in tumour progression [START_REF] Butcher | A tense situation: Forcing tumour progression[END_REF].

Interrogating the homeostatic system

From all of what it has been presented previously, it would seem to derive that understanding the mechanical interplay between the cell and its surrounding is vital for the treatment and prevention of a variety of diseases [START_REF] Handorf | Tissue stiffness dictates development, homeostasis, and disease progression[END_REF]. Unmistakably, we can talk about a dynamic feedback between the internal biochemical contractile machinery and the external active generated forces, as well as a reciprocal force interaction or force feedback loop in between the cell and its environment [START_REF] Handorf | Tissue stiffness dictates development, homeostasis, and disease progression[END_REF]. A better characterization of the mechanical properties of cells and cellular force dynamics can improve the diagnosis of their biological state and the understanding of the pathogenic basis of diseases [START_REF] Suresh | Biomechanics and biophysics of cancer cells[END_REF].

Biochemical and genetic perturbations

Several pharmacologic reagents have become a standard approach at the moment of characterizing the mechanical properties of the cell and its contractility. They consist mainly of small-molecule inhibitors, which are membrane permeable, that target different mechanosensing mechanisms and structures of the cell and are normally supplemented to cell growth medium during experiments. To recover the targeted cellular mechanism, the reagents have to be washed out from the medium.

Blebbistatin has been well-established as a modulator of cell contractility by inhibiting molecular motor myosin II and thus the actomyosin network tension [START_REF] Allingham | The structural basis of blebbistatin inhibition and specificity for myosin II[END_REF].

Polymerization processes of actin can be blocked using latrunculin or cytochalasin D [START_REF] Affinity | Communication[END_REF] or enhanced by using jasplakinolide [63], a reagent known to bind strongly to filamentous actin. Nocodazole is an agent known to depolymerize microtubules and prevent FA disassembly [START_REF] Ezratty | Microtubule-induced focal adhesion disassembly is mediated by dynamin and focal adhesion kinase[END_REF]. The RhoA signalling pathway can be modulated through the use of rho kinase inhibitors such as Y27639 [START_REF] Ishizaki | Pharmacological properties of Y-27632, a specific inhibitor of rho-associated kinases[END_REF] or fasudil [START_REF] Takata | Fasudil, a rho kinase inhibitor, limits motor neuron loss in experimental models of amyotrophic lateral sclerosis[END_REF]. Upstream regulators of myosin phosphorylation such as ML-6 and ML-9 can also be used to modulate cellular contractility [START_REF] Honjo | A myosin light chain kinase inhibitor, ML-9, lowers the intraocular pressure in rabbit eyes[END_REF].

The molecular-genetic methods intended at disrupting the mechanical properties of the cell can target both signalling pathways and structural proteins. This tool uses two main approaches: knockdown, the expression of one or more genes is reduced (with the use of siRNA), and knockout, genetic modification that inactivates an existing gene by replacing it or disrupting it. Therefore, a perturbation can be done in the cellular mechanosensing mechanism by targeting the gene or the mRNA responsible for the studied protein enabling the regulation or inactivation of it [START_REF] Rodriguez | Visualization of mRNA translation in living cells[END_REF]- [START_REF] Chen | Actin-myosin contractility is responsible for the reduced viability of dissociated human embryonic stem cells[END_REF]. The first method is generally reversible, unlike the second one where the targeted gene is disrupted and therefore the cell cannot express it anymore, unless exogenously added.

Physical perturbations

Applying controlled external mechanical stresses to cells in order to study their mechanical properties has been done in many ways for the last forty years.

Techniques have ranged from the conventional micropipette aspiration [START_REF] Schmid-Schönbein | Passive mechanical properties of human leukocytes[END_REF], [START_REF] Evans | Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration[END_REF] and cell poking [START_REF] Goldmann | Mechanical manipulation of animal cells: Cell indentation[END_REF], to deformable culture substrates [START_REF] Vandenburgh | Computer-aided mechanogenesis of skeletal muscle organs from single cells[END_REF] and fluid shear stresses [START_REF] Davies | Mechanical stress mechanisms and the cell. An endothelial paradigm[END_REF], [START_REF] Levesque | The study of rheological effects on vascular endothelial cells in culture[END_REF]. More localized and subcellular mechanical perturbations and force measuring techniques have been made with the use of optical [START_REF] Kuo | Force of single kinesin groups measured with optical tweezers[END_REF] and magnetic [START_REF] Bausch | Measurement of local viscoelasticity and forces in living cells by magnetic tweezers[END_REF] tweezers.

These methods consist on manipulating surface-bound microbeads through the use of optical traps or magnetic fields, allowing the application of mechanical inputs specifically to integrin receptors in the membrane and their linked cytoskeletal counterparts [START_REF] Alenghat | Analysis of cell mechanics in single vinculin-deficient cells using a magnetic tweezer[END_REF].

I would like, however, to focus on the attempts aimed at specifically probing and interrogating the cell tensional homeostatic system that have slowly increased in the recent years. Brown and collaborators presented tissue mechanical response against mechanical loading by using a culture force monitor where precise tensional loads were applied across a fibroblast populated collagen lattice, through a computercontrolled microdrive motor [START_REF] Brown | Tensional homeostasis in dermal fibroblasts: Mechanical responses to mechanical loading in threedimensional substrates[END_REF]. A few years later, Mizutani et al used an elastic deformable substrate to probe single fibroblast stiffness responses and concluded that the cellular mechanical response to deformations was due to actomyosin contractile tension [START_REF] Mizutani | Cellular stiffness response to external deformation: Tensional homeostasis in a single fibroblast[END_REF]. This backed up the idea that dynamical tensional homeostasis was regulated by the tensile forces that phosphorylated myosin would generate on already existing stress fibres, and not on the reorganization of the actin network. In parallel, many studies supported the importance of motor proteins in cell mechanosensitivity and identified myosin II as a main regulator of cytoskeletal tension and, hence a mayor responsible of maintaining tensional homeostasis in dynamic mechanical environment [START_REF] Almeida | Matrix survival signaling: from fibronectin via focal adhesion kinase to c-Jun NH(2)-terminal kinase[END_REF]- [START_REF] Kaunas | Multiple roles for myosin II in tensional homeostasis under mechanical loading[END_REF]. Major matrix stiffening enhances the probabilities of oncogene activation, which may lead to "tumorigenesis". Adapted from [START_REF] Paszek | Tensional homeostasis and the malignant phenotype[END_REF].

With the intention of probing the role of integrins and the signalling pathways known to be involved in cellular contractility (Rho and ERK), Paszek et al subjected tumour cells to a wide range of matrix rigidities (Fig. 8). Their results showed that both signalling molecules are mayor players in the cellular mechanoregulatory system which connects the physical external cues sensed by the integrins, with signalling pathways that mediate cell proliferation and tissue phenotype [START_REF] Paszek | Tensional homeostasis and the malignant phenotype[END_REF]. From these observations they concluded that the cellular tensional homeostasis is favoured in soft matrix but in the event of an abnormal rigidity increase that persists through time, this tensional regulation can be lost leading to malignant transformations in the cells favouring the apparition of a tumour.

Although it had been demonstrated that a cell can respond to mechanical stimuli, little data had been presented to prove that there is a basal internal equilibrium stress state at the single cell level [START_REF] Banes | Mechanoreception at the cellular level: the detection, interpretation, and diversity of responses to mechanical signals[END_REF]. One of the first ones to do so was Fletcher and collaborators using Atomic Force Microscopy (AFM) as a direct force measurement technique, isolating the cell between a patterned substrate and the AFM tip (Fig. 9).

They recorded steady-state cellular forces in time even after imposing mechanical displacement perturbations through controlled movements of the AFM cantilever [START_REF] Webster | Tensional homeostasis in single fibroblasts[END_REF]. substrate and an AFM tip enables both measuring and modulating forces while also imposing displacements, as mechanical perturbations, to individual contracting cells. (B-D) Application of a 1 μm displacement in different time windows shows a force response followed by a tensional stabilization.

Adapted from [START_REF] Webster | Tensional homeostasis in single fibroblasts[END_REF].

Very recently, Zollinger and collaborators also studied the tensional basal state both of single cells and cell clusters through the use of Traction Force Microscopy (Fig. 10).

Measuring the traction forces of cells in a continuous manner, they concluded that the cellular force steady-state is in fact a cell-type dependent phenomenon [START_REF] Zollinger | Dependence of Tensional Homeostasis on Cell Type and on Cell-Cell Interactions[END_REF].

Summary

The evidence showing the relevance of mechanical homeostasis in crucial processes across tissue, cellular and subcellular levels is varied and irrefutable. Tensional homeostatic balance is of great importance for the cell and mechanical forces are one of the main factors controlling it. A better understanding of the major mechanisms involved in modulating cell mechanical responses when faced with external physical stimuli is needed. Much work has been done addressing this issue. However, most of the methods lack molecular specificity in their manner of stress application; they either distort whole cells or large areas of cell membrane. Moreover, many experimental approaches seeking to probe tensional homeostasis at the single cell level have coupled external mechanical perturbations to cell mechanical readouts in a unidirectional manner. But tensional homeostasis relies on the bidirectional coupling between external mechanical cues and internal biochemistry circuits. The overall process implying dynamic feedback loops.

We find that there is still work to be done and there is still a need for much better quantification so that functional interactions can be isolated and established. For this reason we decided to design a novel approach where the perturbation could be made internally, rather than externally, and with very high spatiotemporal resolution under controlled and reproducible conditions. In the following chapter I will present and describe our approach in which we coupled a dynamic input, making use of the emergent and powerful technique of optogenetics, to a dynamic output measuring tool that will record the live cellular mechanical responses, patterned traction cytometry.

CHAPTER 2 -Our approach to interrogate the cellular tensional homeostasis

Introduction

Since our aim was to study the mechanical response of a cell to dynamical and transient tensional perturbations with high-temporal and spatial resolution, we needed a better method than the traditional ones. Physical external probes such as sharp tips or stretchable substrates can provide useful information about the dynamic general cell response to physical stimuli. However, they do not allow the possibility of pulling apart the internal cell tensional mechanism and connecting a perturbation with a specific internal response. Pharmacological perturbations have proven to be very effective at controlling internal nodes but they lack spatial control and temporal flexibility, particularly when considering their reversibility speed and the possibility of using them in multiple off-on cycles [START_REF] Komatsu | Organellespecific, rapid induction of molecular activities and membrane tethering[END_REF], [START_REF] Toettcher | Using optogenetics to interrogate the dynamic control of signal transmission by the Ras/Erk module[END_REF]. Similar limitations are present when using genetic perturbation techniques, such as mutations, knockdowns and siRNAs [START_REF] Loirand | Small GTPases Involvement of Rho GTPases and their regulators in the pathogenesis of hypertension Involvement of Rho GTPases and their regulators in the pathogenesis of hypertension[END_REF], [START_REF] Toettcher | The promise of optogenetics in cell biology: Interrogating molecular circuits in space and time[END_REF]. These are highly specific but relatively slow and broad in their effects with very little to none modulation possibilities causing generally permanent perturbations.

Therefore, we turned our focus towards a more recent and powerful method that offers precise spatio-temporal perturbations and live-cell signalling activity readouts:

optogenetics. In the following section I will briefly review how this approach was developed and the impact it has had in the scientific community. Afterwards, I will describe it in the context of my project.

Optogenetics

It could be argued that using light to interfere in biological structures and processes is not a novelty. Biologists had already been using a few light-based methods to probe biological systems before the appearance of optogenetics. Such is the case of laser ablation and laser inactivation. These techniques enable high spatiotemporal resolution at the moment of inhibiting proteins, by destroying them [START_REF] Sano | Chromophore-assisted laser inactivation -towards a spatiotemporal-functional analysis of proteins, and the ablation of chromatin, organelle and cell function[END_REF], or understanding the role of cellular structures by simply ablating them [START_REF] Rauzi | Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis[END_REF].

However, not only these approaches can entail unwanted cytotoxic effects, but they also lack modular and reversible characteristics. Not to mention the fact that with these tools, biological signals or structures can be disrupted or destroyed but not triggered or induced.

Optogenetics, on the other hand, brought about the possibility of intervening in biological processes in a highly precise, robust, reliable and reversible manner, hence revolutionizing science. Everything started when the Rhodopsins came into play back in the 70s. Rhodopsins are biological light-energy transducers and abundant phototropic mechanisms. They were first found in the early 1970s in the archaeal halophiles where their main function was as proton pumps used to generate a light-driven proton gradient as a source of energy for the cell. However, it was not until the year 2000 when, thanks to metagenomics, they were found in green algae Chlamydomonas reinhardtii [START_REF] Sardari | Study break[END_REF].

This allowed for better isolation and characterization of their function. As a result, in the following years Nagel and collaborators described two membrane channel proteins responsive to blue light which when hit by blue photons, would suffer a conformational change, regulating the flow of positively charged ions [START_REF] Nagel | Channelrhodopsin-1: A light-gated proton channel in green algae[END_REF], [START_REF] Nagel | Channelrhodopsin-2, a directly light-gated cation-selective membrane channel[END_REF].

Having the genetic code for this membrane channel proteins there was no need any more for injecting light-sensitive reagents into cells as they would be the ones expressing them. From then onwards, the bioengineers took the lead. In 2005, Boyden and Deisseroth were the first ones to publish their achievement of using channel rhodopsin II for light-induced firing neurons with unprecedented time and spatial resolution, opening officially a new field: optogenetics [START_REF] Boyden | Millisecond-timescale, genetically targeted optical control of neural activity[END_REF] (Fig. 13). Allowing precise neural activity control, this tool revolutionized neurobiology, consequently being chosen method of the year in 2010 by Nature methods. Adapted from [START_REF] Deisseroth | Controlling the brain with light[END_REF].

Although neuroscience was the first field to exploit and make use of this technique, the versatility and efficiency of the method attracted the rest of the scientific community [START_REF] Deisseroth | Controlling the brain with light[END_REF]. Further tools and approaches where discovered and developed since then, turning optogenetics into a technique that enables real-time precise control of cellular processes, cells, networks and animal behaviour by using lightactivated proteins that affect membrane voltage or intracellular signals [START_REF] Toettcher | Light-based feedback for controlling intracellular signaling dynamics[END_REF].

Several optogenetic systems have been designed to control spatio-temporally the activity distribution of a protein with such accuracy and specificity that activation is possible even at the subcellular scale. Moreover, these light-based perturbative tools fulfil the following properties: reversibility, are rapid and modular, and they allow for a direct readout of light-induced activity. The potential cytotoxicity of this method is almost negligible due to the fact that the light energies and wavelengths used to activate the photo-sensitive systems share the same range as the ones used for optical imaging [START_REF] Toettcher | The promise of optogenetics in cell biology: Interrogating molecular circuits in space and time[END_REF].

The working principle of these systems when subjected to light is based either on the significant conformational change of its main protein or on the high affinity in between two components (Fig. 14). The first case refers to a light-switchable allostery, meaning that the presence of light causes a conformational change on the photosensitive protein that can switch it to its active mode, a membrane channel for example. The second case exploits the association capabilities of two components.

Being one of the two sensitive to light, it will suffer a conformational change when subjected to light that will strongly increase its affinity towards the other component.

Both components by themselves have no signalling or triggering capabilities but can be easily coupled to other proteins or to specific parts of the cell. As a result, a target protein can be localized to a precise part of a cell or two separate components can be brought together to trigger a response through the use of the photosensitive system.

Each of these systems has their practical considerations and has been used based on their advantages and adaptability.

The PHYTOCHROME B (PHYB) protein and PID6.

First one to be used to enable light-controlled protein translocation, described by Levskaya et al [START_REF] Levskaya | Spatiotemporal Control of Cell Signalling Using A Light-Switchable Protein Interaction[END_REF], is an optogenetic system obtained from the Arabidopsis thaliana phytochrome signalling network. Upon red light (650 nm) illumination PHYB binds to its natural interaction partner, phytochrome interaction factor 3 (PIF3), and it dissociates when subjected to infrared light (750 nm). Depending on the biological process under study, the fact that a direct inactivation is needed gives higher control and temporal resolution to the experimentalist. The main issue with this system is the requirement of a chromophore only present in photosynthetic organisms, thus the need to be exogenously added when studying non-photosynthetic systems. protein approach, where the protein under study is expressed as two inactive fragments that upon light absorption reconstitute into a functional protein [START_REF] Kennedy | Rapid blue light induction of protein interaction in living cells[END_REF].

2.2.3

The LOV (Light-oxygen-voltage-sensing) domains.

This optogenetic system consists mainly on the LOV sensory domains which have been described in several different organisms and which also use the ubiquitously expressed endogenous flavin as a chromophore. Hence, these domains are all sensitive to blue light (440-473nm). As a first strategy it can be used allosterically by changing conformation upon blue light and allowing, as a result, the activation of a protein of interest bound to it [START_REF] Wu | A genetically encoded photoactivatable Rac controls the motility of living cells[END_REF]. The second strategy was described by Yazawa et al in 2009 using the blue light-activated dimerization between the LOV protein FKF1

and GIGANTEA, an interacting protein obtained from A. thaliana, to direct the localization of a signalling protein to the membrane in order to trigger a specific signalling cascade [START_REF] Yazawa | Induction of protein-protein interactions in live cells using light[END_REF]. A third strategy consists on using the light-induced homodimerization of a LOV domain bound to DNA, thereby regulating gene expression [102][101].

The pursuit of a smaller system, with enhanced capabilities and tunable properties led, three years later, to the appearance of what Strickland et al decided to call TULIPs. Tunable, light-controlled interacting proteins (TULIPs) derived from the LOV2 domain of Avena sativa phototropin 1 (AsLOV2) and its synthetic interaction with an engineered PDZ domain (ePDZ). Through bioengineering and mutation, TULIPs offer a tunable range of binding and kinetic parameters which makes them easily adaptable to signalling pathways with diverse sensitivity and response times [106].

The Dronpa protein.

This tool is based on fluorescent protein-based interactions that do not need smallmolecule chromophore. Upon light activation (390 nm) the quaternary structure of the Dronpa protein monomer changes inducing a dimerization of the system. The activity of a protein of interest can be modulated by fusing it to a Dronpa monomer and inducing dimerization with light, flanking it and thus inhibiting its function.

Shining light at a wavelength of 490 nm reverses the system to the monomer state reactivating, at the same time, the protein of interest [START_REF] Zhou | Optical control of protein activity by fluorescent protein domains[END_REF]. In contrast with the previously discussed approaches, Dronpa can be used to target proteins that cannot be controlled by relocalization. Moreover, the inherent fluorescence of this protein anticipates the need for an exogenous reporter or biological endpoints, reducing potential variability or delay in measurements [START_REF] Zhou | Optical control of protein activity by fluorescent protein domains[END_REF].

Figure 16 Contrasting the different optogenetic systems described. Adapted from [START_REF] Rost | Optogenetic Tools for Subcellular Applications in Neuroscience[END_REF].

State of the art of optogenetics in mechanobiology

Recapitulating, the optogenetic technique allows for a reliable, robust probing of the system, at the subcellular scale, with precise doses and repetitions, highly modular and reversible, and capable of targeting varying steps in a signalling cascade (Fig. 17). In other words, it enables the opening of the biochemical circuit's black box to study each part of it with precise resolution and in a time-controlled manner. Since its discovery it has been given a diverse range of applications such as, controlling the firing of neurons [START_REF] Boyden | Millisecond-timescale, genetically targeted optical control of neural activity[END_REF], modulating protein activity [START_REF] Park | Protein inactivation by optogenetic trapping in living cells[END_REF], gene expression regulation [START_REF] Konermann | Optical control of mammalian endogenous transcription and epigenetic states[END_REF], [START_REF] Wang | Spatiotemporal control of gene expression by a lightswitchable transgene system[END_REF], inducing signalling cascades [START_REF] Levskaya | Spatiotemporal Control of Cell Signalling Using A Light-Switchable Protein Interaction[END_REF], and even for metabolic engineering processes [START_REF] Zhao | Optogenetic regulation of engineered cellular metabolism for microbial chemical production[END_REF], among others.

It is not surprising then that the field of mechanobiology decided to make use of optogenetic approaches. As it has been discussed in the first chapter, the mechanosensing machinery of the cells consists of both structural components and signalling pathways. With the aim to better understand these intracellular pathways and the interaction of the proteins involved in the cellular mechanical responses, recent work has been done to couple them to optogenetic probes.

At the multicellular scale, a CRY2-CIB1 protein dimerization system was used to better understand the role of cell contractility during embryonic development by inducing cortical actin polymerization and cell contractility through the activation of a phosphoinositide PI(4,5)P2, a regulator of actomyosin contraction [START_REF] Janetopoulos | Phosphoinositide signaling plays a key role in cytokinesis[END_REF]. This approach enabled the analysis of the spatial range of force integration necessary to drive collective contractions and tissue invagination in a drosophila embryo with high spatio-temporal resolution [START_REF] Guglielmi | An Optogenetic Method to Modulate Cell Contractility during Tissue Morphogenesis[END_REF].

Moving to the single cell level, in 2009, Yi Wu and colleagues designed a photoactivatable Rac1 protein to study its activity in cells by sterically blocking its interaction capabilities with a photosensitive LOV domain. Rac1 is one of the main members of the Rho-family GTPases, involved in the regulation of actin cytoskeletal dynamics, ultimately inducing the formation of protrusions rich in actin at the cellular edges [START_REF] Raftopoulou | Cell migration: Rho GTPases lead the way[END_REF]. By reversibly and repeatedly activating Rac1 to drive localized cell protrusions and ruffling, they could better understand the role of Rac activity in the generation of polarized cell movement [START_REF] Wu | A genetically encoded photoactivatable Rac controls the motility of living cells[END_REF]. The scope was extended shortly after to the other two important Rho-family GTPases Cdc42 and RhoA. Cdc42 drives, as well as Rac, the polymerization of branched actin via the activation of Arp2/3, inducing in this case the formation of filopodes and focal adhesion there where the filopodes contact the substrate (Fig. 18). RhoA, on the other hand, regulates the myosin activation, its crosslinking with the actin fibres, the presence of stress fibres enriched in actin and the formation of focal adhesions. Adapted from [START_REF] Wagner | Local RhoA activation induces cytokinetic furrows independent of spindle position and cell cycle stage[END_REF].

As RhoA has also been shown to be involved in cytokinesis, TULIPs were used to gain precise and tight control of RhoA activity, through the photoactivation of RhoGEF, in order to better define the spatiotemporal regulatory logic of the contractile ring assembly at the final stage of cell division [START_REF] Wagner | Local RhoA activation induces cytokinetic furrows independent of spindle position and cell cycle stage[END_REF] (Fig. 19).

All the work previously described had managed to expand our knowledge on how mechanotransductory signalling pathways work and can be regulated. However, not much had been done in understanding the dynamics of cellular force production and the force interaction with the extracellular matrix. To start addressing this, Valon and collaborators designed a system similar to that of Levskaya et al where the GEF catalytic domain responsible for the activation of Cdc42 (Intersectin) [START_REF] Valon | Predictive Spatiotemporal Manipulation of Signaling Perturbations Using Optogenetics[END_REF], or RhoA (RhoGEF) [START_REF] Valon | Optogenetic control of cellular forces and mechanotransduction[END_REF], was recruited to the cellular membrane or the mitochondria membrane. They introduced the CRY2/CIBN optogenetic system in MDCK cells and claimed to obtain a higher recruitment yield compared to PHYB/PIF6 or TULIPs [START_REF] Valon | Predictive Spatiotemporal Manipulation of Signaling Perturbations Using Optogenetics[END_REF] in a reproducible and easy to set up way. Through single and repetitive photoactivations of the RhoA pathways they could measure cellular traction force changes in a non-toxic and highly versatile manner, thus establishing an efficient and reliable tool for interrogating and controlling cell contractility and tissue deformation with a large dynamic range and a temporal control of a few tens of seconds [START_REF] Valon | Optogenetic control of cellular forces and mechanotransduction[END_REF] (Fig. 20). In parallel, Oakes and collaborators used a similar approach but based on the LOV/PDZ interaction, in order to subcellularly activate the RhoA pathway and delve into the dynamics of actomyosin-based force generation [START_REF] Oakes | Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres[END_REF] (Fig. 21). Their experimental result, along with a molecular model presented in their work, demonstrated the elastic behaviour of stress fibres and identified zyxin, an established mechanosensitive protein [START_REF] Yoshigi | Mechanical force mobilizes zyxin from focal adhesions to actin filaments and regulates cytoskeletal reinforcement[END_REF], as a regulator of stress fibre mechanics. The work done by both last authors addressed and restated the tensional homeostatic mechanism present in the cell, while at the same time presented optogenetics as an ideal tool to interrogate such dynamic mechanism.

The optogenetic approach presented in this work is the one developed by Valon et al to characterise RhoA signalling and induce cell contractility and traction forces. I will talk about it in the following section.

Our probing system 2.4.1 The optogenetic set-up: CRY2/CIBN RhoA activation

Briefly recapping, RhoA is a major regulator of cell contractility through the promotion of actin polymerisation via the downstream effector Diaphanous-related formins (Dia) and the phosphorylation of myosins via Rho-associated kinase (ROCK). In addition, the activity of RhoA regulates the enrichment of stress fibres and focal adhesion formation [START_REF] Chrzanowska-Wodnicka | Drives the Contractility Formation of Stress Fibers and Focal Adhesions[END_REF]. Being a clear modulator of the cellular mechanosensing mechanisms, and following the lead of the previously presented works, we decided to focus on the RhoA pathway as a way to interrogate the cellular tensional homeostasis.

To do so we obtained the fibroblast cell line engineered by Leo Valon during his PhD thesis at Dr. Coppey's lab, Curie Institute, Paris. We decided to use fibroblasts as a model cell system based on their normal exposition to tensional inputs in their natural microenvironment, and also due to their previous use in tensional homeostasis experiments. This NIH 3T3 optoARHGEF11 fibroblast cell line has a plasma membrane CRY2/CIBN optogenetic system composed of two proteins expressed by the cell: CIBN-GFP-CAAX (CIBN) localized at the cell membrane with a CAAX anchor and CRY2PHR-mCherry-ARHGEF11 (CRY2), which is initially cytoplasmic. This CRY2/CIBN optogenetic construction to activate RhoA was developed during Dr. Valon's PhD project [123] and used in a scientific publication to activate Cdc42 [START_REF] Valon | Predictive Spatiotemporal Manipulation of Signaling Perturbations Using Optogenetics[END_REF]. Such a system does not require the addition of any exogenous chromophore. When the cell is subjected to blue light (460 nm), CRY2 is recruited to the plasma membrane with a time window of a few seconds (Fig. 22).

Recruitment to the membrane of the nucleotide exchange factor ARHGEF11 triggers the activation of RhoA, which is naturally anchored to the cell membrane by its Cterminus. Taking into consideration the fact that most intracellular signalling pathways are slower than the time of recruitment, the light-induced perturbation can be assumed to be instantaneous [START_REF] Valon | Predictive Spatiotemporal Manipulation of Signaling Perturbations Using Optogenetics[END_REF].

The advantages of using this approach are manifold. In the first place, having a cell transfected with a RhoA activator instead of RhoA itself ensures that, upon blue light, the cell contractile response will be triggered by endogenous levels of RhoA.

Respecting these endogenous levels guarantees that the cell's tensional homeostatic response is the closest to the physiological one [START_REF] Valon | Optogenetic control of cellular forces and mechanotransduction[END_REF]. Secondly, the specificity of the tool ensures no other pathway or secondary protein to be activated apart from RhoA.

Moreover, the amount of activated RhoA is directly proportional to the amount of blue light used, thus allowing for a modulated perturbation and an accordingly modulated homeostatic response. The versatility and reproducibility of the method allows for different activation cycles done on a same single cell without affecting its viability. CIBN. To increase contractility, the translocation of optoGEF-RhoA is forced to the cell surface, where RhoA is located, by targeting CIBN-GFP to the plasma membrane. The system dissociates to its initial state spontaneously. (B) Confocal fluorescence images of a cell with the opto-construct before, during and after light activation. The time scale of maximum membrane recruitment after photo-activation is 20~30 seconds while the dissociation time is 3~5 minutes.

As it was already stated, single cells balance internal and external mechanical stimuli through adhesion and cytoskeletal related forces following a process called tensional homeostasis. In other words, for the cell to maintain a mechanical equilibrium against external perturbations, there has to exist a constant mechanical feedback loop between the cell and the surrounding matrix. This implies that, if we are to interrogate such a system, a dynamic and rapid approach is required, both to induce a perturbation and to record and measure the cellular response. The optogenetic system of choice presents itself as an ideal probing tool, allowing rapid lightmediated perturbations, with low toxicity and fast reversibility. In the following section I will present and describe the method in charge of dynamically measuring the cellular output: time resolved traction force imaging.

Time resolved traction force imaging

Techniques to study and quantify the force interaction between the cell and the extracellular matrix have been under development for the last 40 years. The main readout on which traction force imaging approaches are based is the deformation imposed by the cell onto the substrate to which it is attached. First observations of this were done by the pioneer Harris and co-workers in 1980 (Fig. 23A), where they attempted to quantitatively measure the elastic distortion and wrinkling phenomena occurring when a cell spread over a flexible silicone substrate [START_REF] Harris | Silicone Rubber Substrata : A New Wrinkle in the Study of Cell Locomotion Silicone Rubber Substrata : A New Wrinkle in the Study of Cell Locomotion[END_REF]. Unfortunately, quantitative analysis was very complex due to the non-linearity between the wrinkling and magnitude of the applied cellular traction force. Therefore, suppressing the wrinkles was crucial for a proper analysis. This was finally achieved

Traction force microscopy

Since the seminal work of Lee et al, traction force microscopy became the standard method to study the cellular traction forces produced by stationary or migrating cells on elastic substrates [START_REF] Lee | Traction Forces Generated by Locomting Keratocytes[END_REF]. The transition from glass substrates to elastic substrates was a tipping point in mechanobiology since in their natural environment the most common attachment site for a mammalian cell is another similar cell or the extracellular matrix. Such materials have elastic moduli on the order of 10 to 10.000 Pa against petri dishes which have elastic moduli of 1 GPa [START_REF] Bao | Cell and molecular mechanics of biological materials[END_REF], [START_REF] Wakatsuki | Cell mechanics studied by a reconstituted model tissue[END_REF] (Fig. 24).

Usually consisting of polyacrylamide (PAA) or polydimethylsiloxane (PDMS), these elastic substrates can be tuned to a specific physiologically relevant stiffness and coated with extracellular matrix proteins such as fibronectin or collagen. Adapted from [START_REF] Kolahi | Effect of substrate stiffness on early mouse embryo development[END_REF].

Fluorescent microbeads are embedded close to the surface of the polymer gel and are the markers which will aid the quantitative traction force measurement. When a cell is adhering to the soft substrate it will exert forces through its adhesion sites provoking a deformation. Consequently, as the gel is deformed the microbeads will suffer a displacement from their initial position. Knowing the mechanical properties of the substrate and calculating the microbeads displacement, the cellular traction forces can be reconstructed. In order to achieve this, two images are needed: the image of the beads when the cell is adhering and deforming the substrate and the beads image when the cell has been removed and the gel has elastically returned to its original configuration. The displacement field of the substrate's top surface is obtained when comparing both images. To estimate the traction field, one of the most widely used analytical method is known as the Boussinesq formulation [START_REF] Lifshitz | Theory of Elasticity[END_REF], first adopted by Dembo and Wang [131]. Calculation of the Bousinessq formulation was significantly improved later on by Butler et al by solving the equation using Fourier transform, coining the new term of traction field calculation as Fourier transform traction cytometry (FTTC) [START_REF] Butler | Traction fields, moments, and strain energy that cells exert on their surroundings[END_REF], [START_REF] Tang | A Novel Cell Traction Force Microscopy to Study Multi-Cellular System[END_REF].

TFM theoretical description

The aim of the traction force microscopy technique is to calculate the forces (F) exerted by a cell on a continuous substrate using the deformation measurements. To do that experimentalists need to solve an inverse problem that is ill-posed due to the presence of noise. From this inverse problem solution, it is possible to calculate traction forces at each adhesion site by using linear elasticity theory. Here linear theory of elasticity has been used to calculate the cellular stress field [START_REF] Burton | Traction forces of cytokinesis measured with optically modified elastic substrata[END_REF]. For FTTC calculation the substrate is considered to be homogeneous and a linear elastic semiinfinite half space. The prepared polyacrylamide gel has to be thick enough for this assumption. Both the lateral distance over which displacement is measured, and the lateral dimension of force or deformed area should be small with respect to the substrate thickness in order to approximate semi-infinite elastic continuum to finite one. Thickness of our gels is 70 -80 µm as considered for all experiments. The displacement vector induced by cellular forces at any point can be written as ui on the elastic substrate as convolution form:

Where ui represents the experimental displacement and fj the desired traction field.

The force field includes forces from all other points x apart from the applied point of force. Gij(x) is the Green function which includes the mechanical properties of the substrate used and can be written in index notation as or in full form as Where (1.1)

(1.2) (1.3)
E is the young modulus and ν is the Poisson ratio of the substrate under consideration.

The Green function for the system under consideration has the following properties:

1. It has singularity at the origin.

It varies as 1/r.

This makes the inverse problem of extracting the force more complicated since the 1/r factor has long range effect. Mathematically three standard methods have been established to calculate the force from the displacement field:

1. Boundary element method (BEM) [START_REF] Dembo | Imaging the Traction Stresses Exerted by Locomoting Cells with the Elastic Substratum Method[END_REF].

2. Fourier transform traction cytometry (FTTC) [START_REF] Butler | Traction fields, moments, and strain energy that cells exert on their surroundings[END_REF].

3. Traction reconstruction with point forces (TRPF) [START_REF] Sabass | High resolution traction force microscopy based on experimental and computational advances[END_REF].

BEM technique is based on inverting a large number of linear equations in real space.

Hence it requires long computational time and in exchange a very high resolution can be reached. FTTC method solves the inverse problem in Fourier space which turns out to change the previous convolution (1.1) in a simple matrix multiplication making the computation easy and considerably less time consuming. Some recent advances in the technique called TRPF have been shown by Schwarz et al [START_REF] Schwarz | Calculation of forces at focal adhesions from elastic substrate data: The effect of localized force and the need for regularization[END_REF]. TRPF gives a better accuracy in point force measurement, but it requires a prior knowledge of focal adhesion placements that turns out to add microfabrication steps in the experimental set-up. Comparative study conducted by Sabass et al demonstrated that FTTC, when combined with a proper regularization parameter and filtering, is comparable with results obtained by using BEM0 [START_REF] Sabass | High resolution traction force microscopy based on experimental and computational advances[END_REF].

As one of our goals is to provide statistical measurements, we have chosen to

Displacement field extraction

To determine cell-induced displacement field, the very first step of the analysis is global correction of stage drift using images of beads before (stressed) and after (relaxed) killing the cell. Drift correction is achieved by cross correlating the two images. Position of the maximum peak of cross-correlation corresponds to the global translation. After determining this maximum cross-correlation in between stressed and non-stressed bead images, translation is corrected and bead images are resized to the same dimension. On the first step of displacement field analysis, we perform PIV calculation, where stressed and relaxed bead images are overlapped and subdivided into small windows. Here all the small window sizes are kept constant, typical size of 64 or 128 pixels. Cross-correlation is obtained between the corresponding pair (stressed and relaxed) of bead images [131], [START_REF] Sabass | High resolution traction force microscopy based on experimental and computational advances[END_REF]. Mean displacement is calculated from the peak of the maximum cross-correlated image [START_REF] Butler | Traction fields, moments, and strain energy that cells exert on their surroundings[END_REF], [START_REF] Wang | Focal adhesion kinase is involved in mechanosensing during fibroblast migration[END_REF], [START_REF] Wang | The principles and biological applications of cell traction force microscopy[END_REF], then each bead displacement is mapped using particle tracking in each sub-window. A schematic diagram (Fig. 25) shows the displacement field calculation. The new displacement for each bead turns out to be:

where i corresponds to each PIV window. Xi gives the average displacement in each case and the value of Xi is constant for the all beads on the same PIV window. This calculation needs to determine the bead identity as the displacement can be measured when initial and final position of the beads are known. PIV requires a large enough window to yield accurate values. Therefore, there is a compromise between resolution and accuracy.

(1.4) During particle tracking there will be no ambiguity between a bead and its neighbour in the radius of bead displacement, as large displacements have already been corrected. The accuracy of the measurement will depend on the bead density which translates into a good spatial resolution. These two step processes (PIV and Particle tracking) help to track the beads more accurately. A grid is designed on the displacement field with regular intervals. By interpolation we obtain a field vector on each node of the grid as shown in figure 26.

Traction field determination

As previously described by Butler et al 2002 [START_REF] Butler | Traction fields, moments, and strain energy that cells exert on their surroundings[END_REF] we used Fourier transform (FT) to solve the inverse problem. Thus, matrix convolution equation becomes a simple matrix multiplication. Ğ(k) becomes diagonal in Fourier space. After Fourier transform eq (1.1) becomes:

Where ũ(k), Ğ(k) and ~f(k) are the displacement field, Green's tensor, and force field, respectively, in Fourier space. And k is the wave vector in the Fourier space.

Where

It is easy to calculate Ğ -1 (k) since it is diagonal in Fourier space. The displacement field ũ(k) is calculated by Fourier transform. Since we have obtained the displacement field in regular mesh, it fulfils the requirement of the Fast Fourier transform. Force field is calculated in Fourier space by multiplying the displacement with the inverse of the Boussinesq Green function. It has been shown before that inverse problem is "ill-posed" in the presence of noise and spatial resolution of force can be achieved by adapting a regularization scheme [START_REF] Sabass | High resolution traction force microscopy based on experimental and computational advances[END_REF], [START_REF] Schwarz | Calculation of forces at focal adhesions from elastic substrate data: The effect of localized force and the need for regularization[END_REF]. With the regularization Fourier transform equation becomes:

(1.5)

(1.6) (1.7) (1.8)
For the regularization kernel Ĥij (x-x') 0th order regularization has been chosen.

Finally, force is mapped into real space by inverse fast Fourier transform. After calculation it is then transformed back to the real space by inverse Fourier transform to map the traction force.

In the following figure we present an example of classical traction force calculation with NIH 3T3 cells cultured on non-patterned polyacrylamide gel substrate by using the technique as described before (Fig. 26). To understand more about cell-substrate interaction, contractile or strain energy is also calculated by integrating the traction force times the displacement over the whole area of an individual cell. The strain energy or contractile energy U is equal to the net force applied by the cell on the substrate integrated over the whole projected surface area of the cell. The element of the shear moment matrix can be written as:

In other words, the strain energy represents the energy used by the cell to deform the substrate while the total force represents the non-vectorial sum of each point force exerted by the cell without considering the gel displacement or the cell area. The FFTC technique we have implemented has the advantage to be computationally not intensive. It requires a few seconds to analyse the force field. Making use of PIV and PTV coupled to FTTC technique results in a highly accurate displacement field determination.

Proof of concept -Testing our approach

Having coupled optogenetics as a dynamical input with traction force microscopy as a dynamical output we were ready to interrogate the tensional homeostasis of fibroblasts. Unlike Valon and Oakes, who mainly probed the mechanical responses of either multicellular assemblies or at the subcellular scale, our interest was to focus on the single cell global homeostatic response.

If we consider the mechanosensing machinery of the cell as a closed pre-stressed structure, it follows that an accurate way of studying it is to measure its global response instead of a localized one. In other words, to understand the tensional cellular behaviour as an integrated, hierarchical system rather than as isolated parts.

(1.9)

In figure 27 we present a graph showing the time course of the total force of single cells with a 100 ms photoactivation at t=10 minutes. The cells analysed were freely spreading on a homogenous layer of fibronectin, deposited over a polyacrylamide layer with a Young modulus of 4.47 kPa . Observing the colour code, which identifies different cells with increasing total cell area from blue to red, we could conclude that there is a positive correlation between the basal traction force level and the cell size.

Moreover, when quantifying the relative force increase upon photoactivation of every cell, we found a tendency that would also indicate a positive correlation between cell size and force response.

T At this point, it is worth rising three arguments that will narrow down our study and support the addition of another ingredient to our experimental approach:

1) It has been recorded in the work of both Valon and Oakes that the cellular contractility increase, as a result of photoactivation, does not induce changes in focal adhesion morphology or distribution, at least for the conditions used in those experiments [START_REF] Oakes | Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres[END_REF], [START_REF] Valon | Optogenetic control of cellular forces and mechanotransduction[END_REF].

2) The work done by Mizutani and collaborators concluded that the mechanical cellular responses to the induced physical perturbations originated with the contractile tension generated by the stress fibres. This would imply that the dynamical tensional homeostasis is carried out mainly by the actomyosin network [START_REF] Mizutani | Cellular stiffness response to external deformation: Tensional homeostasis in a single fibroblast[END_REF].

3) The findings of Valon and Oakes also showed that light stimulation does not induce de novo stress fibre formation, hence implying that the dynamic mechanical homeostatic response could mainly be modulated by the already existent actomyosin network, and not by a reorganization or reassembly of it [START_REF] Oakes | Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres[END_REF], [START_REF] Valon | Optogenetic control of cellular forces and mechanotransduction[END_REF].

As a matter of fact, the cellular actomyosin skeleton is not a randomly arranged network. Work done on cell shape and actin organization [START_REF] Oakes | Geometry regulates traction stresses in adherent cells[END_REF], [START_REF] Tseng | A new micropatterning method of soft substrates reveals that different tumorigenic signals can promote or reduce cell contraction levels[END_REF], along with results obtained during this project, show that depending on the cell geometry, size and matrix rigidity, actin filaments and stress fibres present a certain level of order and organization (Fig. 28). The geometry and mechanics of the cellular environment impact on cell architecture and play a notable role by modulating the forces produced by cells. The aim of this project is to study the spatio-temporal tensional homeostatic response of a cell to dynamic perturbations of its internal signaling pathway. It has been shown that a main regulator of this mechanical response is the actomyosin network.

However, considering that this network depends on factors such as size, geometry and rigidity, and that tensional homeostasis intrinsically relates tensional balance to cell shape regulation, the interplay between internal machinery perturbations and external forces generations would appear to be best studied in situations where cell shape can be controlled. In this way we can actually manage to narrow down possible variables, being able then to examine effects of single parameters that are often coupled. As a result of this we can better understand the link between cellular force and stress energy dynamics with the actomyosin network arrangement. For that purpose and through the use of micropatterning techniques, we introduced a new component to our experimental approach that would impose specific geometrical constraints: patterned traction cytometry.

Patterned traction cytometry

This approach couples microfabrication techniques with force imaging. Using a combination of cell micropatterning and traction force microscopy on soft elastic substrates it is possible to systematically probe the existing relation in between cell shape and cell force generation in response to ECM physical properties.

Micropatterning

Microfabrication is a very useful approach in cell mechanics as well as in fluid mechanics. The main interest for researchers relies on the possibility to design model environments with fixed boundary conditions (micropatterns, microwells, micropillars etc.). By designing the artificial environment, cell internal organization and multi-cellular assemblies can then be modulated enabling at the same time a statistical analysis of cell morphological behavior.

The geometry and architecture of the external matrix surrounding the cell can be mimicked and tailored using surface micropatterning. This technique is based on the fabrication of extracellular matrix (ECM) protein patches of controlled size and shape, called micropatterns, surrounded by antifouling polymers which prevent the cell or other proteins from nonspecific adhesion (Fig. 29). It has been widely shown that the cell adhesive microenvironment geometry regulates many vital physiological processes such as cell shape, internal cell organization, cell fate, differentiation, etc.

[35], [START_REF] Vignaud | Polyacrylamide Hydrogel Micropatterning[END_REF]. Studies have proven that cell shape plays a role in various cellular processes, such as focal adhesion assembly [START_REF] Chen | Cell shape provides global control of focal adhesion assembly[END_REF] or stem cell lineage commitment [START_REF] Mcbeath | Cell shape, cytoskeletal tension, and RhoA regulate stemm cell lineage commitment[END_REF]. The micropatterning technique used is based on the one already described by Vignaud et al [START_REF] Vignaud | Polyacrylamide Hydrogel Micropatterning[END_REF]. During the procedure the patterned soft substrate is obtained directly from the photomask, ensuring in this way a very high spatial resolution. The patterning process is efficient at large scales. The great interest of this technique is thus to fabricate tens of thousands of patterns at a time on the same coverslip. The patterning substrate of choice is polyacrylamide hydrogel (PAA), the rigidity of which can be modulated to very low Young modulus, around 0.5 Pa and higher up to 40 kPa, by controlling the concentration of the acrylamide and bis-acrylamide used for polymerization.

The interest of working with polyacrylamide gels is manifold:

1. Polyacrylamide (PAA) is a soft elastic material that allows experimentalists to measure cellular tractions forces.

2. PAA is very transparent enabling imaging through the gel.

3. PAA is very easy to prepare.

4. PAA is mechanically very stable and its mechanical properties can be easily tuned.

5. PAA material is biocompatible.

In recent years, micropatterning on soft substrates [START_REF] Wrobel | Micropatterning tractional forces in living cells[END_REF], [START_REF] Damljanović | Bulk and micropatterned conjugation of extracellular matrix proteins to characterized polyacrylamide substrates for cell mechanotransduction assays[END_REF] has enabled the study of traction forces associated with a given cell shape. Consequently, traction forces were found to increase with the cell spreading area [START_REF] Reinhart-King | Endothelial Cell Traction Forces on RGD-Derivatized Polyarylamide Substrata[END_REF], [START_REF] Tan | Cells lying on a bed of microneedles: An approach to isolate mechanical force[END_REF] and cellular force distribution was shown to be strongly affected by the cell aspect ratio [START_REF] Gavara | Mapping cell-matrix stresses during stretch reveals inelastic reorganization of the cytoskeleton[END_REF], [START_REF] Rape | The regulation of traction force in relation to cell shape and focal adhesions[END_REF]. All of these studies where done on soft substrates using adhesive patterns with convex shapes, such as full disks, squares or rectangles [START_REF] Kilian | Geometric cues for directing the differentiation of mesenchymal stem cells[END_REF], [START_REF] Mandal | Cell dipole behaviour revealed by ECM sub-cellular geometry[END_REF]. Such patterns made it possible to control the overall shape and area of cell envelope. Considering that both the spatial organization of the ECM protein and the substrate stiffness have consequences for cell physiology it is logical to combine both in order to faithfully reproduce and control cell microenvironment [START_REF] Vignaud | Polyacrylamide Hydrogel Micropatterning[END_REF].

Chapter 3 -Results and model

Tuning the set-up

The starting point of our experimental quest was to corroborate some of the statements done during the introduction. In the first place, we needed to confirm the existence of a basal tensional level in a cell constrained to a micropattern. As far as we knew, the main record of this had been presented by Webster and colleagues when studying the tensional homeostasis in single fibroblast, by constraining the cell in between an AFM cantilever tip and a fibronectin coated micropatterned substrate [START_REF] Webster | Tensional homeostasis in single fibroblasts[END_REF]. The following step would be to tune and characterize the optogenetic system, verifying the onset of contractile episodes upon light activation and testing the reproducibility and modularity of the approach. The confirmation of the previous steps would then enable us to start the tensional homeostasis interrogation and its connection with the actomyosin network.

Choosing the micro-pattern geometry

We fabricated soft substrate micropatterns with high spatial resolution to constrain the cell under study to a specific adhesive geometry which would remain virtually unaffected. The geometry of choice was a full circle or disk-shaped micropattern with a projected area of 1000 um 2 . The choice of geometry was not arbitrary. Studies have shown that micropatterns that present corners or asymmetric geometries can modulate the polarity and organization of the cellular actomyosin network [START_REF] Mandal | Cell dipole behaviour revealed by ECM sub-cellular geometry[END_REF]- [START_REF] Jiang | Directing cell migration with asymmetric micropatterns[END_REF] (Fig. 30), hence imposing a bias on the cytoskeletal tension. It is in our interest to study the cells dynamic tensional homeostasis and its actomyosin network with the least number of pre-imposed mechanical stresses. For this reason, we designed a circular micropattern where we expected the cell to present a more unbiased behavior [START_REF] Parker | Directional control of lamellipodia extension by constraining cell shape and orienting cell tractional forces[END_REF]. Studying only cells which covered the full extension of the disk-shaped micropattern, we used live traction force microscopy to record the tensional state of a cell throughout time and static traction force microscopy to obtain higher statistical data.

In parallel, we used phalloidin to stain the actin cytoskeleton and study the stress fibres organization. Observing the cellular force and stress maps together with the actin staining (Fig. 31) we encountered our first striking result. Being in a completely symmetric shape, we had expected the cell to present isotropic force behavior and a random actin distribution. From the force and stress images obtained we could see a

polarized cell with what it seemed a bipolar force pattern. This was further supported by the fact that the stress fibres presented a clear direction of alignment instead of a random disorganized one. In order to better quantify and characterize this potential polarized behavior of the constrained cell we decided to calculate the first order moment of the force distribution [START_REF] Butler | Traction fields, moments, and strain energy that cells exert on their surroundings[END_REF], also known as force dipole. This is defined as a 2x2 tensor Mij, which has energy dimensions and describes the contraction/dilation forces as well as the torque applied by the cell. The elements Mij are obtained by integrating the coordinate ri times the traction stress Tj over the cell envelope:

𝑀 𝑖𝑗 = ∫ 𝑟 𝑖 𝑇 𝑗 (𝒓)𝑑𝒓
Since the net torque exerted by the cell is expected to be zero, the matrix M is symmetrical in theory. Hence, it is possible to find the principal contractile axes by applying a rotation operator to obtain a diagonal matrix. In this description, the force distribution is reduced to two contractile dipoles along the two principal directions (Fig. 32).

Practically, the first order moment tensor M is calculated from the experimental traction map for individual cells and the dominant orientation is determined from the direction of the eigenvector corresponding to the largest eigenvalue. This direction should indicate the cell orientation in the case of a polarized force pattern (for further information please see [START_REF] Mandal | Cell dipole behaviour revealed by ECM sub-cellular geometry[END_REF]). From a population of 135 cells we found a mean value for the polarization degree of 0.1928. This result is not strong enough to consider that cells on the studied micropattern present a high polarization. However, it showed that even when constrained to a completely symmetric geometry the cell will still attempt to polarize and align in a specific direction.

Tensional homeostasis in a constrained cell

To record the live tensional state of cells on the circular micropattern we used live traction force microscopy. Pictures of the cell and the microbeads embedded on the soft gel were taken every 20 seconds during a period of 52 minutes. The stack of images obtained from that experiment was used to reconstruct the traction forces exerted by the cell on the substrate during that time window. A total of 23 cells were studied and their tensional profile was obtained and graphed. Both the non-vectorial sum of all the forces exerted by the cell (Total force) and the strain energy are shown.

In the graphs of figure 34 we can see an average of the studied cell population showing a steady-state in the cellular forces with time, thus confirming the concept of a stable tensional homeostasis. The averaged strain energy showed a mean value of 2.086e-13 ± 7.996e-015 J and a variation coefficient of 3.83%, and the averaged total force showed a mean value of 434.1 ± 9.150 nN and a variation coefficient of 2.11%.

Both force and stress values were consistent with previous observations [START_REF] Oakes | Geometry regulates traction stresses in adherent cells[END_REF], [START_REF] Wang | The principles and biological applications of cell traction force microscopy[END_REF], [START_REF] Tseng | A new micropatterning method of soft substrates reveals that different tumorigenic signals can promote or reduce cell contraction levels[END_REF], [START_REF] Mandal | Cell dipole behaviour revealed by ECM sub-cellular geometry[END_REF]. The coefficient of variation shows the extent of variability in relation to the mean of the population and it's a good measure of how much the tensional level fluctuates.

It is important to point out that this stability was studied in the course of 52 minutes were none of the cells suffered cell division or detachment from the micropattern.

Vianay et al have very recently shown that traction forces vary as the cell goes

through its natural cycle of division [START_REF] Vianay | Variation in traction forces during cell cycle progression[END_REF]. We can corroborate, from the discussed results and for non-dividing cells in the time window studied, the existence of a stable cell tensional state that is not affected or hampered by constraining the cell to a micropattern. We can now carry on with the photo-perturbations.

Tuning the optogenetic system

As it was described on Chapter 2, the experimental approach used involves a CRY2/CIBN optogenetic system, developed originally by Dr. Valon at the Curie Institute in Paris [START_REF] Valon | Predictive Spatiotemporal Manipulation of Signaling Perturbations Using Optogenetics[END_REF]. Upon blue light activation, this system relocalizes the nucleotide exchange factor ARHGEF11 to the cell membrane bringing it closer to RhoA and, consequently, triggering the activation of the RhoA signaling cascade.

However, there is an extra feature in this optogenetic construction which consists of a mCherry reporter linked to the CRY2 molecule. It gives the advantage of testing the system to confirm the interaction of the CRY2/CIBN couple before tackling the analysis of the RhoA activation. An increase of mCherry fluorescence in the membrane and a depletion of it in the cytoplasm right after photo-activation, confirms the well-functioning of the optogenetic system (Fig. 35). Failure to see such recruitment would imply that the cell has lost the optogenetic construct and further analysis is futile. Once the CRY2 recruitment to the membrane upon light activation was confirmed, we could address the contractile response of the cell to the photo-perturbation.

In the following two graphs on figure 36, we present the two main experiments aiming at tuning and characterizing the optogenetic system. In the first graph we can see the averaged strain energy profile of 7 individual cells being subjected to a 50 ms pulse of blue light followed by another one of the same exposure time 15 minutes later. Not only there is a clear response to the perturbation and a return to the tensional homeostatic level, but there is also an evident reproducibility and robustness in the method.

T im e ( m in ) shown in Dr. Valon's work [123], where the recruitment intensity increases with the

S

Mechanical adaptation to area changes and perturbations

As presented at the end of Chapter 2, during the analysis of the tensional dynamic response on freely spread cells, we found a positive correlation between the basal traction force level and the cell size. Moreover, when quantifying the relative force increase upon photoactivation of every cell, we found also a tendency that would indicate a positive correlation between cell size and force dynamic response to perturbation.

Following the concept that tensional homeostasis intrinsically relates tensional balance to cell shape regulation, these findings led us to include the micropatterning technique as part of the experimental approach with the aim to better quantify the cellular contractile behavior and narrow down the variables. Constraining the cell to a specific geometry would enable us to better regulate both the size ranges and parameters involved in the cellular mechanical response of the actomyosin network, such as cellular size and shape. With the aim to repeat the experiment done on freely spread cells with varying spread areas in a more controlled manner, we decided to use 3 disk-shaped micropatterns of increasing surface area: 500 um 2 , 1000 um 2 and 1500 um 2 .

In Figure 38 The first result when studying the live basal contractile state of individual cells spread on each of the 3 sizes showed 3 defined strain energy levels in a time window of 56 minutes (Fig. 39 A). It could already be concluded that changing the size did not affect the force regulation and tensional homeostasis of the cell. It did, however, change the basal level values for each size. We observed a strain energy mean value of 7.121e-014 ± 5.638e-015 J for cells on 500 um 2 disk with a coefficient of variation of 7.92%. Cells on 1500 um 2 presented average strain energy of 5.139e-013 ± 9.977e-015 J with coefficient of variation of 1.94%.

When analyzing a larger set of cells through static force microscopy (Fig. 39 B) we obtained higher variability but we still found 3 significantly different strain energy levels. The mean contractile level was 3.422e-014 ± 2.039e-014 J, 2.446e-013 ± 1.513e-013 J and 3.198e-013 ± 1.575e-013 J for 500 μm2, 1000 μm2 and 1500 μm2 disk-shaped patterns, respectively. Regarding the coefficient of variation we calculated the values 59.58%, 61.87% and 49.26% for 500 um2, 1000 um2 and 1500 um2 disk-shaped patterns, respectively.

The increase in cellular basal tension associated with size increase has been interestingly discussed by Wang and collaborators who described the cell as an active mechanical structure with a certain level of pre-stress [START_REF] Wang | Mechanical behavior in living cells consistent with the tensegrity model[END_REF]. This active stress is exerted by the actomyosin network even in the absence of an externally applied force and, in other words, could be considered as none other than the cellular tensional homeostasis. However, this pre-stress is directly related to the cell's shape and size and thus whenever the active structure, in this case the cell, suffers an increase in shape, it will necessarily suffer an increase in internal pre-stress. What we see in our results would appear to be consistent with this statement. This photoperturbation induced an averaged cellular contractile energy maximum increase of 9.068e-014 ± 4.883e-014 J, 3.005e-013 ± 1.659e-013 J and 4.262e-013 ± 3.251e-013 J for cells on 500 μm 2 , 1000 μm 2 and 1500 μm 2 respectively. The time to peak was of 2.56 ± 0.67 min, 3.61 ± 0.72 min and 3.25 ± 1.35 min with a relaxation time of 4.47 ± 1.2 min, 5.71 ± 1.45 min and 5.97 ± 0.72 min for cells on 500 um 2 , 1000 um 2 and 1500 um 2 respectively. It could be confirmed that the change in cell size did not affect its potential of recovering the basal tensional state. Interestingly, it could also be observed that the higher pre-stressed state of cells on larger patterns did not prevent or diminished its force response capabilities. As it had been seen with the freely spread cells, the cell's contractile response was higher for cells on larger disk-shaped micropatterns.

T The question that we had to pose ourselves after obtaining these results was whether the spreading size was the only explanation to the differences in the force levels and responses or if there was any variation in the internal tensional mechanism being also involved.

Since it had been mentioned many times that there is a direct link between the active cellular internal stress and the actomyosin network, a better way to understand the obtained force dynamic readouts was to study what was happening with the cellular contractile machinery.

A statistical analysis of the actin network organization in phalloidin inmunostained cells gave an interesting outcome. To study the arrangement of stress fibers in the cells we implemented a software that calculates the local orientation of actin stress fibres and renders an 'order parameter'. This parameter represents how parallel the local orientation of each actin stress fibre is to the average orientation. The closer to 1 means the more aligned the fibres are with each other (a more detailed description of this parameter can be found in the Materials and Methods Appendix). When analyzing the cells on the 3 disk-shaped patterns we found a trend that implied a positive correlation between the size and the internal actin alignment (Fig. 41). This trend had been seen in the cases were the micropattern changed, elongating the cell [START_REF] Oakes | Geometry regulates traction stresses in adherent cells[END_REF]. However, this finding meant that even when the geometry and shape envelope of the cell was preserved, the size increase was altering the internal actin alignment, hence possibly modifying the actomyosin contractile network dynamics. In order to go one step deeper in the actomyosin network analysis we decided to record its behavior in live mode and verify if the photo-activations where inducing actin rearrangements. To track the stress fibers throughout the photo-perturbation protocol we incubated the cells under study with SiR-actin. Based on the fluorophore silicon rhodamine and the actin binding natural product jasplakinolide, Sir-actin allows the labelling of filamentous actin in live cells with high specificity and low background [START_REF] Lukinavičius | Fluorogenic probes for live-cell imaging of the cytoskeleton[END_REF]. Videos done recording the cellular stress fibres while the cell was being photo-activated supported the data presented by Valon et al and Oakes et al.

While photo-activation induced an increase in the intensity of labeled stress fibres (not so evident when doing global photo-activation), implying a reinforcement of these structures, it did not prompt the rearrangement of the actomyosin network (Fig. 42). Our main goal was to interrogate the dynamic tensional homeostasis to better understand the response of the actomyosin network to the internal perturbations induced by photoactivation. In order to do so, we had to narrow down possible variables that would be linked to that response such as shape, migration potential and rigidity. However, as it could be concluded from the order parameter, there also seemed to exist a link between the actomyosin network dynamics and the cell size.

This led us to pose ourselves a new question: Can we uncouple those parameters inducing a different actin alignment independently from the cell spread area? If we could achieve that then the dynamic tensional interrogation would be directly addressed to the actomyosin network arrangement.

Decoupling area from actin organization in cellular response to photoperturbation

It has been shown that cells with similar shape maintain the same contractile state regardless of the adhesive geometry [START_REF] Mandal | Cell dipole behaviour revealed by ECM sub-cellular geometry[END_REF], [START_REF] Albert | Dynamics of cell shape and forces on micropatterned substrates predicted by a cellular Potts model[END_REF]. Nevertheless, as far as we are concerned the dynamics of this global state and its response against a mechanical perturbation have not been addressed. We would like to probe that contractile state in single cells with the same shape but modifying their actomyosin alignment. In other words, we want to keep the same adhesion area and cell envelope while affecting the actin architecture and understand how that could impact on the tensional homeostasis dynamics.

As we found for the case of the 1000 μm 2 disk-shaped micropatterns (hereinafter referred as Disk), the actin and stress fibers alignment is considerable. Basing our conclusion strictly on the order parameter, cells spread on Disk present high actin alignment. What would happen with the cellular mechanical response if we could keep the shape and size of the cell while reducing the internal actin alignment? At what level does the actomyosin network arrangement affects the cell's contractile response to perturbations?

Searching for the actin troublemaker

Taking advantage of the versatility of microfabrication and micropatterning we designed different potential candidates (Fig. 43). We had seen through own experience and scientific publications [START_REF] Tseng | A new micropatterning method of soft substrates reveals that different tumorigenic signals can promote or reduce cell contraction levels[END_REF], [START_REF] Mandal | Cell dipole behaviour revealed by ECM sub-cellular geometry[END_REF], [START_REF] Théry | Cell distribution of stress fibres in response to the geometry of the adhesive environment[END_REF], [START_REF] Kassianidou | Geometry and network connectivity govern the mechanics of stress fibers[END_REF], that subcellular geometries and non-adhesive borders can induce particular actin arrangements.

Based on this knowledge we designed 10 different micropatterns which imposed the On 4 of those patterns we decided to maintain the same adhesive contour while including different internal potential anchoring points that would affect the actin networking, the idea being that those points would add branching points in the network and also decrease the number of long and aligned stress fibers. For the rest we also modified the adhesive boundary to modulate and modify the available anchoring points (focal adhesions) of stress fibers that span the whole cell body.

Studying the actin network of the cells on each of these patterns led us to a promising result. Even though a few of the geometries would induce cellular actin misalignment, only one of them would do it in a stable, reproducible, repetitive and significant way. The need for reproducible and stable misalignment was not a minor issue considering the fact that having most of the fluorescence spectra dedicated to photo-activation, micropatterns and microbeads, the possibility of tracking the cellular actin while coupling light stimulations with traction force measurements was not experimentally achievable. As it can be observed on figure 43, the micropattern that resembles a 3-spoked wheel with a discontinuous contour (hereinafter referred as Wheel) imposed what could be lightly called a triangular actin arrangement with 3 main stress fiber orientations. A qualitative idea of this can be obtained by observing the averaged actin stained images, where the internal geometry is still visible, implying that most of the stress fibers adopt the mentioned triangular arrangement instead of going over the "spokes".

A more quantitative approach was done by comparing the order parameter obtained for cells spread on all the shapes designed. In the graph of Figure 44 The 'stability' of the actin disarrangement imposed on the cell by the wheel shape was followed and corroborated with the use of live SiR-actin stained cells. As it can be observed for a representative cell in Figure 45, it maintained the 'triangular actin arrangement' aforementioned throughout a period of 10 hours. Finally, the comparison of the order parameter between the Disk and the Wheel showed a significantly lower global actin alignment for cells spread on the second micropattern (Fig. 46). Having found the desired actin troublemaker we moved to the following step of characterizing its tensional behaviour.

Force and tensional characterization of the confronted patterns

Using live and static traction force microscopy we analyzed the tensional homeostasis of cells spread on the Wheel and contrasted it afterwards with the data obtained for cells on the Disk. Consistent with what had been discussed regarding cells with same shape and size, the unperturbed tensional state of cells on the Wheel was similar to the ones on the Disk with no significant differences (Fig. 47).

Averaging the basal strain energy of 23 cells spread on the Wheel shape we obtained a mean value of 2.289e-013 ± 5.686e-015 J with a coefficient of variation of 2.48% (for the disk we had measured an average strain energy of 2.086e-13 ± 7.996e-015 J). The static traction force analysis showed a mean contractile level of 2,341e-013 ± 1,046e-013 J and 2,199e-013 ± 9,662e-014 J for cells on Wheel and Disk, respectively.

This result not only supported the claim that cell's with similar projected area presented the same tensional baseline, but also proved that the degree of order of the cellular actomyosin network doesn't appear to affect such baseline. On the other hand, a clear tripolar force pattern could be appreciated on cells spread on Wheel in contrast to the more dipolar force pattern seen already on the Disk.

T Indeed, even when this result was expected, based on what was discussed regarding cells with same size and envelope, it was paramount for our intentions of decoupling the cellular size and shape variables from the actomyosin network arrangement. Now, this last parameter could be linked to the cellular response against perturbation in a more clear and straightforward way.

Actomyosin alignment response to perturbation

Having a confirmed and significant difference between the stress fibres alignment on cells on Disk against those on Wheel, we performed photo-activation pulses on both cases. Results obtained after photo-perturbation with 100 ms time exposure light pulse revealed a difference in the magnitude of tensional response in between the two cases (Fig. 48). Cells spread both on the Disk and on the Wheel presented a force increase upon light activation and a subsequent return to tensional equilibrium. The This was a remarkable result considering the fact that we had shown that cells on both shapes had a similar basal tensional state. On top of that, such steady-state value had neither been modified by the available subcellular spreading area nor by the internal actin global alignment. The difference appeared when disrupting the cellular mechanical equilibrium, forcing the cell to contract. In the event of a photoperturbation, the actin arrangement would be controlling the efficiency of force production in terms of the amplitude of the induced perturbation.

Our observations led us to the realization that the concept of tensional homeostasis needs to be characterized both in an unperturbed state as well as during a perturbed one. While the system parameters may not modify the steady-state, they could determine the out-of-equilibrium dynamics.

The conclusion that we could draw from our specific findings is that the cell's contractile machinery performance is susceptible to the internal actin order in a clear significant way. The arrangement of stress fibers and the actin organization strongly modulates the dynamic cellular force response.

Modelling the experimental data

In order to obtain a quantitative experimental recapitulation and a better understanding of the cell's tensional responses, a mechano-biophysical model was constructed by the theoreticians Dr. Ulrich Schwarz and Dimitri Probst from the Institute for Theoretical Physics in Heidelberg, Germany.

Briefly stated, the model considers the cell as a Kelvin-Voigt viscoelastic system with an elastic component, represented by Ec, and a viscous component, represented by η (Fig. 49). Both components are parallel to each other giving the material a damped response behavior against any instantaneous signal. An active stress component σ is included in the system. This stress tensor represents the "background stress" (σback) that the cell exerts on the substrate, i.e. the homeostatic cellular tensional state, plus the stress contribution that occurs upon photoactivation (σph). The substrate to which the cell is attached is represented as springs of constant density Y and is non-zero at any place of the pattern where the cell can actually create anchoring points.

A B

This active Kelvin-Voigt model as a mechanical representation of the cell was used to fit the experimental curves obtained for both the disks of varying sizes (500 μm 2 , 1000 μm 2 and 1500 μm 2 ) and the Wheel, and also to characterize times of activation and relaxation. A full description of the model and the data obtained can be found in the Appendix C.

Supporting our findings 3.11.1 Decoupling adhesive area from actomyosin organization

The main feedback obtained when presenting this work to the scientific community was the question whether there was an actual correlation between the contractile response and the available spreading area. Was it safe to claim that the responsible for the lower force production was mainly the actin alignment? An available spreading area disparity of 570 μm 2 in the Wheel against the 1000 μm 2 offered by the Disk could very possibly be another reason for this force response difference, as this could be having a significant impact on focal adhesion distribution and stress fiber anchoring points.

One ring to rule them all (the findings)

To tackle this matter and put our findings to the test we went back to our previously designed micropatterns to see if we could find the proper compromise that would decouple the adhesive area from the actomyosin organization. We were looking for a shape that would maintain a high actin alignment as the Disk while having a similar adhesive area as the Wheel. Observing the results obtained for the previous shapes we considered that the best candidate for the control experiments would be the Ring (Fig. 50), an 'empty' circular micropattern with an available spreading area of 630.75 μm 2 , a closer area value to that one of the Wheel: 570 μm 2 . The stress map obtained for cells on the Ring showed a similar dipolar pattern to that one seen for cells on the Disk. In the same manner, we found the actin alignment to be comparable in cells on both shapes. The graph of Figure 51 shows no significant difference in the order parameter of cells on Disk and Ring, and a clear difference with the Wheel.

Response to photo-perturbation for cells on Ring and focal adhesions comparison

Using a light pulse of 100 ms exposure time we probed the response of 10 cells on Ring to contrast it with the already obtained data for cells on Disk and Wheel (Fig. 52). With a mean strain energy increase of 3.741e-013 ± 1.869e-013 J, cells on the Ring presented a significant higher contractile response against photo-stimulation than those on the Wheel but no significant difference with those on the Disk. This result would seem to support our previous statement linking actin alignment to force response. However, another variable that had to be looked at was how the focal adhesions were being affected by the shape and available spreading area differences.

Was there any variation in the focal adhesions size or quantity that could account for the contractile response differences observed?

To answer this we performed vinculin staining assays on cells spread on the 3 patterns (Fig. 53). Vinculin is a cytoskeletal protein present in the focal adhesion complex involved in the link between integrins and filamentous actin [START_REF] Burridge | Microinjection and localization of a 130K protein in living fibroblasts: a relationship to actin and fibronectin[END_REF]. Staining of this protein has been a standard way of focal adhesion characterization.

The analysis gave some interesting results. Observing the vinculin stained cells individually showed a similar trend in the morphology and orientation of the focal adhesion to that one seen on the actin stained cells. Elongated focal adhesions in cells on Ring and Disk showed high alignment in one preferred direction while those in cells on Wheel seemed to follow the already mentioned 'triangular arrangement'. On the other hand, the statistical analysis proved that with a mean total area of 64.07 Taken together, results obtained from graphs A and B of Figure 54 showed that there was no significant difference in the size and amount of focal adhesions present in cells spread on any of the 3 shapes. This would be confirming the major role of the actin organization in the force production response.

Saturation phenomena after multiple photoactivations of increasing intensity

In order to further characterize the optogenetic system and the cell contractile responses to varying photo-activations, we tried out one last experiment. We carried out a similar light protocol used by Dr. Valon (Fig. 37) when studying the CRY2/mCherry membrane recruitment, which consisted on increasing the exposure time of the light pulses in the following order: 10 ms, 20 ms, 50 ms, 100 ms, 150 ms, 200 ms (Fig. 55). Results obtained from this experience showed that the cell's contractile response reached a saturation point at 100 ms time exposure light pulse. Such behaviour did not follow the same trend reported by Dr. Valon, where the signal of CRY2/mCherry recruitment to the membrane increased all along the protocol. This would imply that no matter the increase of RhoGEF to the membrane, the cell reached its force maximum response after a stimulation of 100 ms of blue light. The saturation was corroborated repeating the activation protocol for cells on the Wheel (Fig. 56). Cells However, it is not clear if tensional homeostasis on a single cell level corresponds to a well-defined tension setpoint or not. The main obstacle to progress in this direction is the lack of appropriate techniques to dynamically vary the stresses in cells. Traditional approaches in biology use pharmacological or genetic approaches to perturb cell contractility, but these are typically slow and hard to control in a quantitative manner. Direct application of physical force has an immediate effect, but tends to be a strong perturbation to the biological system. Combining micropatterning with an AFM-setup to dynamically measure and control forces, it has been shown that single cell tension evolves towards a plateau, but that this setpoint is variable and depends on the history of mechanical loading (Webster BPH 2014). While cells maintained tension during slow loading, they strongly pulled back during fast loading. In order to quantify TH for single cells in a less intrusive manner, a more flexible and configurable approach is needed to rapidly and dynamically change cell forces. The optimal solution in fact would be a direct manipulation of the regulatory machinery for contractility inside cells. This dynamic control can in fact be achieved with optogenetics (Deisseroth et al, 2011). Here we combined optogenetics, to induce cell contractility, with traction force microscopy, to measure the strain energy that cells impart to their environment, thus achieving an immediate relation between cell input and output. Moreover, as cell forces are closely related to cell shape, we performed our experiments on micropatterned substrates, to uncouple our findings from cell shape modulation effects. Our experimental data on living cells show that individual cells maintain a constant setpoint of tension, but that it strongly depends on cell size and actin organization. By changing the actin cytoskeleton organization through micropatterning while keeping similar cell envelope and spreading area, we were able to show that actin architecture has a decisive role in determining cellular force production efficiency. As confirmed by a theoretical model for actively contracting thin films with different domains, maximal efficiency is obtained only for completely polarized cells. Force generation is in addition limited by the biochemistry of Rho-activation, as shown here by systematically varying activation time.

T im e ( m in

Larger cells display a higher strain energy production in response to transient RhoA perturbations

To investigate how cells react to fast transient perturbations, we coupled time resolved force imaging with optogenetic stimulations. Our strategy was to trigger the activation of the small GTPase RhoA, the major regulator of cellular contraction (ref Alan Hall). We used previously described NIH3T3 cells stably expressing a Cry2-CIBN optogenetic probe to dynamically control the localization of ArhGEF11, an upstream regulator of RhoA, by using blue light [Valon et al., 2014]. To limit our measurements from cell shape variability, we used soft micropatterning to restrict cells to predefined areas and shapes (Figure 1a). An established mathematical model that describes the physical core of this situation is the continuum mechanics of a thin contractile film of the same geometry (Figure 1b) Tseng-Balland LabChip 2011, Oakes BiophysJ 2012] and also as predicted by the standard model (solid line in Figure 1c). The slight differences between experiment and model can be understood from the fact that the actin organization changes in a non-linear fashion with cell size, with actin organization saturating with increased size as measured by the actin order parameter (Figure 1d).

(
Upon photo-activation (100 ms blue light pulse) cell strain energy quickly increased (~2 minutes) before slowly relaxing (6 to 8 minutes) (Figure 1e), in good agreement with earlier reports (Valon BPJ). Most importantly in the context of TH, cell strain energy recovered its original baseline level, confirming the concept of a stable setpoint in tension. We measured an average strain energy baseline of 0.0801 ± 0.0005 pJ, 0.2622 ± 0.0009 pJ and 0.4501 ± 0.0010 pJ on small (500 µm²), medium (1000 µm²) and large (1500 µm²) micropatterns, respectively (Figure 1e), reflecting the higher pre-stress induced by cell spreading area (Figure 1c) and in good agreement with the model predictions. We then quantified the Relative Strain energy Increase upon photoactivation (RSI, maximum peak value minus baseline strain energy). Surprisingly, pre-stressed cells were not limited in their traction efficiency as they were able to generate even higher contractility. The RSI upon a 100 ms blue light stimulation was only 0.0907 ± 0.0173 pJ for cells spread on small micropatterns, but reached 0.3005 ± 0.0627 pJ and 0.4262 ± 0.1150 pJ on medium and large micropatterns, respectively (Fgiure f, error values are expressed as SEM). These results could be reproduced by our model by assuming a double-sigmoidal activation of the active stresses, as suggested by earlier experiments (Valon BPJ). In our simple model, we then also obtained increasing energy gains with increasing cell size. Together, these results validate the concept of TH and show that a simple model can explain the main experimental results. However, Figure 1d also suggests a role of the actin organization that is not reflected by the model. We therefore set out to investigate this point in more detail by using a larger variety of different micropatterns.

Actin polarity determines the efficiency of force production during optogenetic activation

In order to investigate the relationship between the organization of the actin cytoskeleton and efficiency in cellular forces production, we designed a circular micropattern with three branches, hereafter named the "wheel" micropattern (Figure 2a). This micropattern led to a projected cell area similar to its discoidal counterpart while inducing a different organization of the actin cytoskeleton (Figure 2b). Because cells on the disc patterns break the circular symmetry and spontaneously polarize in one direction, the wheel pattern is effectively more isotropic, as it enforces three different domains with pairwise balance each other. In order to adapt the standard model to this actin organization, we divided the computational domain in different parts, each with the main direction of actin orientation determining the direction of the anisotropic stress (Figure 2c). Surprisingly, such a model gives similar strain energies, in very good agreement with the experimental results and in line with the concept of TH. Interestingly, the experiments also revealed a smaller variance on the wheel pattern. Unexpectedly, however, we measured a different response to blue light stimulation on cells spread on disc versus wheel micropatterns (Figure 2d). The speed of cell contraction was similar on both micropatterns, however, cells on discs, presenting an anisotropic, dipolar actin cytoskeleton, exerted a greater response to photo-activation in terms of force amplitude, with a time to peak of 3.43 ± 0.83 min and a RSI of 0.3536 ± 0.05898 pJ. Cells on wheel patterns, with a more isotropic, tripolar actin organization, responded with a time to peak of 2.71 ± 1.02 min and a RSI of 0.1853 ± 0.02386 pJ. We also verified that the observed responses in terms of force production were not impacted by differences in the fibronectin adhesive area allocated to the cells. To this end we used a ring shaped micropattern that has an adhesive area close to the wheel micropattern and measure both adhesive expression of the cells and the efficiency of their force production. We found no significant differences in the total area occupied by focal adhesion on the three different shapes (see SI). Interestingly the ring shaped micropattern induced an actin organization close to the one observed in the discoidal pattern case. Strikingly the force dynamic response to the optogenetic stimulus was fairly identical for ring and disc patterns demonstrating the main role of the organization of the actin cytoskeleton in the efficiency of force production. Strain energy increase for every activated cell on the two different shapes. Calculation is made by subtracting the strain energy value before activation to the highest strain energy value obtained after light activation.

Figure SI Cells with similar actin organization display identical force response

To be written

Materials and methods

TFM gel preparation -MASK METHOD

Description of the procedure based on the work done by Vignaud, Hajer Ennomani, and [START_REF] Vignaud | Polyacrylamide Hydrogel Micropatterning[END_REF] with modifications done at Motiv group.

A photomask (TOPAN), previously rinsed with water and isopropanol, and a glass coverslip (20 mm) are activated together with air plasma (4 minutes) and oxygen plasma (40 seconds). Then a pLL-PEG drop (35 µl) is sandwiched between the chrome side of the mask and the glass coverslip. After 30 min incubation, the glass coverslip is removed and saved for the following step as it is now a passivated surface. The photomask is exposed to deep UV during 3 minutes from the quartz side, burning the pLL-PEG at defined loci with minimum loss of resolution due to diffraction. Then again, a drop (35 µl) of sodium bicarbonate (100 mM) solution of fibronectin (20 ug/ml, Sigma) and Alexa546conjugated fibrinogen (5 ug/ml, Invitrogen) is sandwiched between the mask and the passivated glass coverslip and incubated for 30 min. For 4.47 kPa hydrogels, a solution containing 12.5% acrylamide (from 40% stock solution) and 7.5% bisacrylamide (from 2% stock solution) was prepared in a 10 mM DPBS solution (pH 7.4). Finally, the polyacrylamide solution is mixed with passivated fluorescent beads (0.2 um, Invitrogen) by sonication before addition of ammonium persulfate (APS)

and N,N,N',N'-tetramethylethylenediamine (TEMED). A drop (47 µl) of this solution is sandwiched between the patterned region of the mask and a silanized glass coverslip. After 30 min polymerization, the coverslip with the hydrogel is carefully removed from the mask and stored in DPBS solution at 4 °C. Cells were plated on them the following day.

For each pixel in the cell, the structure tensor J (that has 3 elements: J11, J12 and J22) is computed in a local neighbourhood that is also Gaussian. The orientation angle, the coherency and a measure of local gradient (grey level is constant or it changes) are computed from the elements of the structure tensor (λi are the eigenvalues of J):

The average orientation and order parameter S will be computed by averaging over all pixels for which the coherency is above a threshold value, which can be changed.

Average angle: θm=〈θ〉c>thres

Order parameter: S=〈cos(2(θ-θm))〉c>thres (S=1 means that the local orientation is parallel to the average orientation, S=0 means that they are orthogonal).

Vinculin staining

After 4 h of culture on the micropatterns, cells were fixed with 3.7% formaldehyde in PBS, permeabilized with 0.2% Triton X-100 in TBS (50 mM Tris-HCl, 0.15 M NaCl, pH 7.4) and blocked with 2% BSA (Sigma Aldrich) in TBS. The samples were then incubated with primary antibodies against vinculin (Sigma Aldrich) and detected with Alexa 488-conjugated, isotype-specific, anti-IgG antibodies (Invitrogen). Actin was labelled with phalloidin-TRITC (Sigma) and nuclei were stained with DAPI (Life Technologies).

Areas of focal adhesions were segmented and measured by using a home-made Image J (National Institutes of Health) routine.

Traction force microscopy

Displacement fields describing the deformation of the polyacrylamide substrate are determined from the analysis of fluorescent beads images before and after removal of the adhering cells with trypsin treatment. The displacement field can be obtained by merging the images of the gel under stress, that means while the cell is alive, and the non-stressed image, which is after the cell has been detached using trypsin. Its calculation is made by a two-step method consisting of particle image velocimetry followed by individual bead tracking [START_REF] Sabass | High resolution traction force microscopy based on experimental and computational advances[END_REF][START_REF] Butler | Traction fields, moments, and strain energy that cells exert on their surroundings[END_REF]. Force reconstruction was conducted with the assumption that the substrate is a linear elastic half-space, using Fourier Transform Traction Cytometry (FTTC) with zeroth-order regularization [START_REF] Sabass | High resolution traction force microscopy based on experimental and computational advances[END_REF]). The shear modulus of the gels used in these experiments was 4,47 kPa. All calculations and image processing were performed in Matlab combining particle image velocimetry and single particle tracking.

Chapter 4 -Discussion and conclusions

Discussion

Tensional homeostasis is a fascinating and intriguing concept in the field of mechanobiology that has received increasing attention as its dysregulation has an important contribution to pathological conditions, such as developmental defects, cardiovascular and pulmonary diseases, and cancer [START_REF] Wyatt | A question of time: Tissue adaptation to mechanical forces[END_REF], [START_REF] Chien | Mechanotransduction and endothelial cell homeostasis: the wisdom of the cell[END_REF], [START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF], [START_REF] Paszek | Tensional homeostasis and the malignant phenotype[END_REF]. In environments where mechanical modifications and perturbations are common, stresses and strains can accumulate, and lead to tissue deformations that can significantly affect tissue integrity and structures. In consequence, a better understanding of how cell/tissue maintains a stable physiological state against intrinsic and extrinsic mechanical perturbations is of utmost importance.

Although this concept of mechanical integrity preservation is broadly understood and accepted, I would like to draw the discussion towards the fact that being a developing term, the concept of tensional homeostasis is the target of interesting

debates both in open discussions and in the bibliography. Idea exchanges with collaborators and colleagues have evidenced the existing dilemma in what is actually meant by single cell tensional homeostasis, if there is such a thing and whether there is a more accurate way of referring to the active process under study.

In the first place a study done by Canovic et al concluded that tensional homeostasis was a multicellular phenomenon and that "it may require a higher level of organization than that of a single cell" [START_REF] Canovic | Tensional homeostasis in endothelial cells is a multicellular phenomenon[END_REF]. Such a claim introduced controversy in the scientific community as Webster et al and Weng et al, among others, had presented it also as a single cell process in previous publications, the last ones using the term mechanical homeostasis. Considering that Canovic had used endothelial cells and previously mentioned studies had worked with isolated fibroblasts, further work within the same group led to a recent study by Zollinger and colleagues where different cell types were compared. In their attempt to clear out if tensional homeostasis started at the cellular, multicellular or tissue level they studied the temporal fluctuations of traction forces in isolated and clustered endothelial, fibroblasts and vascular smooth cells. Their conclusion was that the phenomenon of single cell tensional homeostasis does exist, but is cell-type dependent [START_REF] Zollinger | Dependence of Tensional Homeostasis on Cell Type and on Cell-Cell Interactions[END_REF].

Other variables have also been shown to impact on the cellular tensional homeostasis. Paszek and collaborators when studying how tissue stiffness could modulate the onset of tumor-malignant behaviour, showed that substrate rigidity impacted significantly on the homeostasis-related cell mechanosensing processes [START_REF] Paszek | Tensional homeostasis and the malignant phenotype[END_REF]. This dependence with the substrate rigidity was also seen in preliminary results

obtained at the end of this project where basal tension levels would vary with different substrate stiffness. Moreover, results presented in the previous chapter showed that such a variation was also happening when increasing cellular sizes, implying that single cell tensional homeostasis is also a size-dependent phenomenon.

A final criticism to this apparently unclear homeostatic concept was done by Webster et al. when studying the tensional steady state of single fibroblasts and their response to perturbations with an elegant approach [START_REF] Webster | Tensional homeostasis in single fibroblasts[END_REF]. Isolating the cells between a micropatterned substrate and an AFM tip they would both measure and modulate forces while also imposing displacements, as mechanical perturbations, to individual contracting cells. Their experiments showed that, after cell displacement perturbation, the cellular contractility did not return to the original basal level but instead reached a new one, increased after a positive strain and reduced after a negative strain. This shifting compensation in the cell contractile state led the authors to redefine the concept of tensional homeostasis with what they decided to call tensional buffering.

Instead of focusing on the details and the parameters of the perturbations chosen for that experiment, which could also give material for discussion, I would like to point out one of the concluding remarks of Tensional buffering does appear as a more accurate definition, but I would dare to say that although it considers the tensional compensations that the cell presents against perturbations, it disregards the fact that the cell will attempt to go back to the basal state as long as the external environment is still the same. That is what homeostasis is understood as, "an active promotion of equilibrium by biological systems" [START_REF] Humphrey | Vascular adaptation and mechanical homeostasis at tissue, cellular, and subcellular levels[END_REF].

My take in this debate is that tensional homeostasis should be regarded as the way that the cells have to adapt their tensional state, within the desired properties, to the mechanical environment by means of feedback loops. It is a description that also tries to embrace Mina Bissell's idea of dynamical reciprocity as it can evolve in the event of permanent external modifications. This definition implies inevitably a more general concept than a fixed setpoint.

As a consequence, such an interpretation could lead to the conclusion that the tensional homeostasis is not a very accurate and scientifically relevant term considering its dependence on so many factors. However, the fact that it might be too much of a general concept does not prevent possible further characterization and understanding of the mechanisms involved in such process. It is in this light that we aimed at narrowing down the variables to test the dynamics of the homeostatic responses. We probed the contractile reaction of the single fibroblast to photoperturbations while modifying the cellular size and the internal network arrangement. As a consequence, we were able to 'normalize' the basal level and just interrogate the active process involved in recovering it.

At this point, it is an undeniable fact that every healthy, non-dividing cell has a certain internal tensional equilibrium.

Conclusion

The aim of this thesis project was to delve into the phenomenon of tensional In more specific project-related terms, results confirmed the existence of a basal contractile state in non-dividing fibroblasts, which was preserved against mechanical perturbations and has been lately referred to as tensional homeostasis. This state was maintained throughout experiments that lasted up to 90 minutes and which involved photo-perturbations of increasing intensities. Moreover, studying cells with different spreading areas showed that this tensional equilibrium still occurred and increasing the cell size increased its basal value. However, this increase in the internal 'prestress' of the cell didn't prevent a proportional stress response against photoperturbations. This result would imply that the cells spreading area modulates the process of tensional homeostasis. Coupled with this result we also observed a positive correlation between the increase in the actomyosin network alignment and the cell size. Inspired by these findings we aimed at probing the possible link in between the stress fibers alignment and the tensional homeostasis responses to perturbation. To do this, we kept the cell size unchanged in order to keep the same basal tensional state, but modified the global cellular actin arrangement through the design of particular sub-cellular patterning geometries. Results showed a significant decrease in the cellular contractile response to the same perturbation for cells with lower stress fibers alignment. A higher actin alignment translated to a higher force production upon perturbation. This outcome led us to the conclusion that the arrangement of stress fibers and the actin organization have a strong impact on the dynamic cellular force response.

A good analogy to illustrate this concept can be made with a tissue that is present in most complex biological systems, the skeletal muscle. The fine alignment between myofibrils bundled in the fibers that make up skeletal muscle is a clear example of efficient force production through high ordered organization. In the same way, a cell with highly aligned stress fibers can exert higher force responses than one where the actomyosin network presents a lower global alignment.

• Since APS is not very stable, one aliquot was used for each experiment and the remaining solution was systematically discarded.

Mask treatment; cleaning and activation • Dip the mask in a Pyrex with Electroscrub for 5 min rubbing the mask on the chromium side constantly using gloves. This process should be performed under a chemical hood with appropriate user protection.

• After the 5 min, rinse the mask with plenty of deionized water. Dry the mask with nitrogen air gun.

• Rinse both sides of the mask with isopropanol and then dry the liquid carefully using nitrogen gas.

• Use 20mmx20mm coverslips and using the air gun make sure they are dust free before the plasma activation.

• Use megahertz plasma cleaner at 100% power.

• Pre-clean the empty plasma cleaner by running air plasma at 0.2-0.3 mbar pressure during 3 minutes.

• Put the mask (chromium side facing the air) and the coverslips in the plasma cleaner.

• Start pumping out the air in the reactor and wait for the pressure to stabilize at 0.3 mbar.

• Open the air inlet and let plenty of air flow for a minute.

• Pump out the air in the reactor and wait for the pressure to stabilize at 0.3 mbar.

• Run the plasma at 100% power for 4 min.

• Inject plenty of oxygen for a minute.

• Pump out the oxygen in the reactor and wait for the pressure to stabilize at 0.3 mbar.

• Run the plasma at 100% power for 1 min.

• Close the gas inlet, stop pumping, and ventilate the reactor (a filter should be placed on the air inlet to avoid dust intake into the reactor).

pLL-PEG quartz mask coating • Put one drop of pLL-PEG solution (25 mL/cm2) on the region of interest on the mask. For the case of 20x20mm coverslips you should use 35 μl, and for the 32 mm round coverslips use 70 μl.

• Cover the drop by flipping the activated glass coverslip on it and let it incubate for 30 min.

• Meanwhile, prepare a solution of NaHCO3 pH 8.3. Dissolve 420 mg of sodium bicarbonate in 50 ml of miliQ water using a 50 ml falcon tube.

• At the end of the incubation, lift the coverslips carefully without scratching the coating on the photomask. Leave the coverslips drying face up on a kimwipe. As the coverslips have been coated at the same time we will keep them for the incubation with the ECM protein; they will provide a fully passivized surface that will be used to sandwich the ECM droplet on the activated mask after UV insolation.

• Put the photomask vertically. The solution should run off by itself. Rinse with pll-peg/HEPES and let it dry. Be careful to remember which size has been coated with pLL-PEG to prevent any damage on this side.

Deep UV insolation and protein coating • At this step, we will burn the passivized surface at specific positions by shining UV light through the chrome photomask from the non-passivized side. The UV light will burn the passivized treatment directly on the mask and this will then allow the adsorption of protein at these specific positions.

• Heat up the UV lamp. This is very important. Power measurements of the lamp have shown that the steady state power is reached after 2-5 min depending on the age of the lamp. We usually let it run for 5 min and then immediately put the sample inside the lamp and start the insolation process. The power measured at steady state was 6 mW/cm2 at a distance of 1 cm from the lamp and a wavelength of 190 nm (you should take care to control the power frequently).

• Flip the mask to have the coated side away from the UV source. You can use small holders on the squares of the mask to prevent scratching of the coating. Expose to UV for 3 min.

• Prepare protein coating solution: we use a solution of 20 mg/ml of fibronectin diluted in sodium bicarbonate 100 mM. A small amount of fluorescently labeled protein could be added in order to see the micropatterns by fluorescence microscopy. Store the solution on ice.

• For the coating solution use 2 μl of fibronectin dilution, 2 μl of fluorescently labeled protein (fibrinogen) and 96 μl of the NaHCO3 solution previously prepared.

• Remove the mask from the UV lamp and set it on a horizontal surface, passivized side now facing up.

• Put a droplet of protein solution (25 ml/cm 2 ) on the region of interest (35 μl for the case of the 20x20 mm coverslips) and then put the pLL-PEG coated coverslips saved previously on the top, passivized side facing the droplet. Protect from light and let it incubate for 30 min.

• In the meantime, aliquot the desired amount of acrylamide solution and put it to degas in a vacuum bell.

• At the end of the incubation, remove the glass coverslips and discard them. Having the mask horizontally, pour some bicarbonate solution on it to rinse. Afterwards, put the mask vertically and pour some more bicarbonate solution on the coated spots. Let the solution dry by itself.

Transfer on acrylamide gel • Here we will polymerize the acrylamide gel sandwiched between the patterned photomask and the silanized coverslips. During detachment, the gel will stay attached to the silanized coverslip and the protein from the patterned mask will be transferred to the free surface of the acrylamide gel, resulting in a micropatterned acrylamide surface.

• Set the photomask horizontally with the pattern side facing up. Make sure that you have waited long enough for the solution to dry.

• Collect the acrylamide solution from the vacuum bell and keep the container closed.

• Optional: If you want to add some fluorescent beads in your gel for force measurements, they should be added at this stage (0.4 μl) of the process in the acrylamide solution and the solution should be sonicated for 3 min to destroy any bead aggregates that could have formed during the storage.

• Prepare TEMED and APS and the silanized coverslips. You will add TEMED and APS solution to the acrylamide with the following proportions: 1 ml of TEMED and 1 ml of APS 10% for 165 ml of acrylamide solution. You should proceed as fast as possible in the next steps.

• First, add TEMED to the acrylamide solution, briefly but vigorously mix.

• Second, add APS solution to the acrylamide solution, briefly but vigorously mix.

• Put a drop of 7 ml/cm 2 of the acrylamide polymerization mix on the mask in each patterned area of interest. For the case of the 32 mm diameter round coverslips, you should add 47 μl of the mix.

• Slowly place the silanized coverslip on top while taking care to avoid bubbles.

• Put a cap (to prevent evaporation) and let the gel polymerize for 30 min. Keep the rest of acrylamide in a closed container as a control of gel polymerization.

• Once the polymerization is finished (you should check it by detaching the remaining acrylamide from the tube, it should have the shape of the container and be elastic if you try to pinch it with a pipette tip), cover the coverslips with PBS and let the gel hydrate for 2 min.

• Detach the acrylamide gel by very carefully lifting the silanized coverslip using a razor blade. To do that you should first detach gently all around the coverslip until it comes off by itself. Due to the silanization process, the gel will stay attached to the coverslip. Make sure that the gel is fully immersed during the entire detachment process otherwise you will end up with collapsed micropatterns.

• Rinse the acrylamide gel attached to silanized coverslip (acrylamide coverslips) in PBS several times.

• Control quality with fluorescence microscope if possible.

• Store at 4° C and use within a week.

Mask cleaning

• Start the mask cleaning process while it is still wet with PBS. Do not let it dry otherwise the polyacrylamide will be harder to remove afterwards.

• Use water, soap and a sponge if possible and clean the mask thoroughly. Dry with nitrogen gas gun.

• Rinse both sides with acetone. Dry with nitrogen gas gun.

• Rinse both sides with isopropanol. Dry with nitrogen gas gun.

• Pre-clean the empty plasma cleaner by running air plasma at 0.2-0.3 mbar pressure during 3 minutes.

• Put the mask (chromium side facing the air) in the plasma cleaner.

• Start pumping out the air in the reactor and wait for the pressure to stabilize at 0.3 mbar.

• Open the O2 inlet and let plenty of oxygen flow for 10 minutes. (Oxygen plasma has a much higher cleaning efficiency than air plasma).

• Pump out the O2 in the reactor and wait for the pressure to stabilize at 0.3 mbar.

• Run the O2 plasma at 100% power for 15 min.

• Close the gas inlet, stop pumping, and ventilate the reactor.

• Store the mask in a dust free environment.

Oxygen plasma (Wikipedia)

If the gas used is oxygen, the plasma is an effective, economical, environmentally safe method for critical cleaning. The VUV energy is very effective in the breaking of most organic bonds (i.e., C-H, C-C, C=C, C-O, and C-N) of surface contaminants. This helps to break apart high molecular weight contaminants. A second cleaning action is carried out by the oxygen species created in the plasma (O2+, O2-, O3, O, O+, O-, ionised ozone, metastable excited oxygen, and free electrons). These species react with organic contaminants to form H2O, CO, CO2, and lower molecular weight hydrocarbons. These compounds have relatively high vapour pressures and are evacuated from the chamber during processing. The resulting surface is ultra-clean.

Cell culture and plating

Stable cell line NIH 3T3 fibroblasts with CIBN-GFP-CAAX and optoGEF-RhoA constructs (kindly provided by L. Valon and M. Copper, Insitut Curie, Paris, France) were cultured in Dulbecco's Modified Essential Medium (DMEM) containing 10% foetal bovine serum (FBS) and 0.2% penicillinstreptomycin. Cells were grown in a humidified 5% CO2 incubator at 37ºC. Cells were seeded on patterned substrates at a density of 200.000 cells/cm 3 . All traction force measurements or immunostainings were performed 4 hours after seeding to ensure full spreading of the cells. Leibovitz's L-15 medium, supplemented with 10% FBS and 0.2% penicillin-streptomycin, was used as imaging media for every live imaging experiment.

Live cell imaging and activation

Cell imaging and activation intended for posterior force measurements was carried out using a Nikon Ti-E microscope, Zyla sCMOS camera (Andor, Belfast, UK) and Plan Apo VC 60x/1.40 Oil objective (Nikon). The microscope was equipped with an incubator that maintains the temperature at 37 °C. Global cellular photoactivation was performed using a LED light source (X-Cite/XLED1, Lumen Dynamics, Canada) coupled to a Mosaic digital micromirror device (Andor). Depending on the experiment done, activation pulses were 10-20-50-100-150-200 ms long using an LED at 460 nm with power of 256.7 uW (measured at the back focal plane of the objective).

Traction force microscopy

Cellular traction force is the physical force exerted by cells on the extracellular matrix. At present, traction force microscopy (TFM) is an efficient and reliable method to determine the cellular traction forces acting on a flat flexible substrate. For that purpose, fluorescent trackers are embedded in the substrate during its fabrication. The key concept of traditional TFM is the acquisition of a pair of ''before kill'' and ''after kill'' microscopy images (hereafter referred to as BK image and AK image, respectively). A BK image is a fluorescence image of the deformation of soft substrates caused by cells, and an AK image is a fluorescence image of non-deformed elastic substrates taken at the same location by detaching the cell through trypsinization. The displacement field can be obtained by merging the images of the gel under stress, that means while the cell is alive, and the non-stressed image, which is after the cell has been detached using trypsin. The composite image reveals the areas in which the cell exerts a force and displaces the beads. For the analysis of the displacement a Matlab program which combines particle image velocimetry and single particle tracking is used. By tracking the movements of the fluorescent trackers, and knowing the mechanical properties of the substrate, one can derive the force field applied on the substrate.

Four hours after plating, the culture medium was discarded, gels where placed on microscope chamber and CO2 independent medium was added. After placing the chamber on the microscope stage, the gel was manually scanned and each properly spread cell was photographed in brightfield, far red, and mCherry mode. Afterwards, the culture medium was retrieved and 2 ml of trypsin were added. Five minutes later the medium was flushed to remove the cells from their original position and A B C

Figure 60 The complex machinery that transmits the mechanical perturbations from the environment to the nucleus. External forces are sensed by the integrins at the focal adhesions, information that is then transferred to the actomyosin network that is physically connected to the nucleus LINC complex, which delivers the information to the internal part of the nucleus potentially altering its functions and activating or regulating gene expression. Adapted from [START_REF] Wang | Mechanotransduction at a distance: Mechanically coupling the extracellular matrix with the nucleus[END_REF].

My contribution to this work consisted mainly on performing image analysis to obtain the cellular force readouts using static force microscopy and providing line micropatterns for 1D migration studies.

Traction force measurements showed that even though mammalian fibroblasts without nucleus (cytoplasts) and cells with nuclear lamina defects were able to exert forces, these were considerably lower than those of intact control cells. Similarly, cytoplasts sensed mechanical cues, such as rigidity variations, but responded in an impaired way. These observations implied that the nucleus plays a fundamental role in the mechanotransduction of the cell. In parallel, results showed that enucleated cells were capable of polarizing and migrating in 1D lines and 2D environments, but not in 3D environments.

Overall, the data obtained suggested that normal cell polarization occurs independently of the nucleus, but the regulation of normal cell contractility and mechanosensing is nucleus dependent.

In the following pages you will find the publication in its published format.

Figure 1 A

 1 Figure 1 A) Claude Bernard (left) and Walter Cannon (right). B) Graphic simplified representation of the homeostatic process where the system fluctuates, within an accepted range, around an 'ideal'

Figure 3

 3 Figure3Extracellular matrix influences in cellular mechanic responses. Mechanical interactions between the cell and its environment can be divided into three main categories. A normal loading situation is where forces applied by the ECM are correctly countered by the cell resulting in the maintenance of a physiological tensional state. An overloading, such as an abnormal remodelling of the ECM, can exceed the limits of tensional response of the cell, resulting in a pathological response such as fibrosis. A degradation or loss in the mechanical properties of the ECM can induce the cell into apoptosis. Adapted from[START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF].

Figure 5

 5 Figure 5 Simplified graphic depiction of the key signalling pathways connected to integrin activation in the cellular mechanosensing processes. Transmembrane receptors known as integrins mediate the external mechanical interaction between the cell and the ECM while at the same time being in direct contact with the internal signalling molecules that also make up the focal adhesion complexes. Upon mechanical stimulation (communicated by the integrins) these signalling molecules will trigger the signalling cascades MAPK and Rho that will lead to gene regulation at the nucleus, and mechanical responses from the actomyosin network, ultimately affecting posterior cellular response and adaptation. Adapted from[START_REF] Humphrey | Mechanotransduction and extracellular matrix homeostasis[END_REF].

Figure 6

 6 Figure 6 Graphic depiction of how the stress and physical stimuli from the cellular environment impact on the physiological state of the cell. Similar to what it was depicted on Figure3, this condensed graph shows a minimum of cellular apoptosis when the stress that the cell senses is within the homeostatic range, and an increase in cell death outside this range. Adapted from[START_REF] Chan | Mechanostasis in apoptosis and medicine[END_REF].

Figure 7

 7 Figure 7 Stem cells differentiation towards adipocytes or osteoblasts based on geometrical constraints. (A) Quantification of cells captured on rectangles of varying aspect ratio differentiating to adipocytes or osteoblast lineage. (B) Quantification of cells differentiating to either lineage when captured on fivefold symmetric shape. Adapted from [55].

Figure 8

 8 Figure 8 Scheme showing the dependence of the tumour-malignant transformation with the exogenous stiffness evidencing the ERK-and RHO-mechanoregulatory circuits. An increase in the extracellular matrix stiffness prompts focal adhesion formation and subsequent activation of both Rho and ERK, ultimately resulting in inner cellular tension. Major matrix stiffening enhances the probabilities of oncogene activation, which may lead to "tumorigenesis". Adapted from[START_REF] Paszek | Tensional homeostasis and the malignant phenotype[END_REF].

Figure 9

 9 Figure 9 Stable tensional state and response to displacement perturbations in isolated fibroblasts. (A) Depiction of the probing device. Isolating the cells between a micropatterned

Figure 10

 10 Figure 10 Temporal fluctuations of traction forces in isolated and clustered cells of different types. (a-b) The normalized contractile moment of isolated endothelial cells presents significantly higher fluctuations than for the case of clusters. (c-f) Both fibroblasts and vascular smooth cells present steady state contractility at the single cell and multicellular scale. Forces were obtained using Force Traction Microscopy and each colour represents a different cell. The results obtained implied that the phenomenon of tensional homeostasis is cell-type dependent. Scale bars, 25 μm. Adapted from [87].

Figure 11

 11 Figure 11 Single cell mechanical homeostasis dynamics at the subcellular level. (a) Depiction of a single cell suffering a mechanical perturbation followed by the homeostatic process of regaining mechanical equilibrium. (b) Fibroblasts spread on the microposts and SEM image of the cell-micropost attachment corresponding to the white rectangle. Scale bar, 20 μm. (c) Upper row shows subcellular forces (yellow arrows) exerted on the microposts (red dots) before, during and after the mechanical stimuli. Lower row shows the fluorescently stained focal adhesions corresponding to the upper row images during the same states. The colour-coded arrowheads identify the changes in force and focal adhesions variations during mechanical stimulation. Scale bar, 10 μm. Adapted from [88].

Figure 12

 12 Figure 12 Optogenetic system plugged to the head of a mouse. By selectively inserting opsinswhich react to light-into them, neurons can be activated or inactivated for research purposes Then, when light shines on the brain through optic fibres, only those neurons will respond and induce a certain behaviour in the studied animal. Early behavioural applications of the technique induced mice to act in certain, easily observable ways (left). A simplified graphical representation of a light-gated ion channel activated by light (right). (Source: Optogenetic methods Julich, John B. Carnett/GETTY).

Figure 13

 13 Figure 13 Working principles of optogenetics. Electrical stimulation would induce a generalized action potential in the neuron axons that are in the vicinity of the electrode. Optogenetic allows for a selective excitation or inhibition of neurons action potential happening only on photosensitive cells.Adapted from[START_REF] Deisseroth | Controlling the brain with light[END_REF].

Figure 14

 14 Figure 14 Different optogenetic approaches depending on the process studied and the photosensitive protein. Adapted from [101].

Figure 15

 15 Figure 15 Proposed applications for three most widely used photosensory proteins: LOV domains, cryptochromes and phytochromes. Adapted from[START_REF] Kim | Optobiology: optical control of biological processes via protein engineering[END_REF].

Figure 17

 17 Figure 17 Benefits of optogenetic approaches in cell signalling and biochemistry. (a) Targeting a specific node in a signalling pathway to better understand the intermediates involved in it. (b) Possibility of studying single cell response avoiding distortion of data from multiple heterogeneous cells. (c) Being a reproducible and non-toxic method, the same cell can be probed in different conditions and be used as its own control. (d) The intensity of light stimulation can be modulated, hence obtaining a modulated activity or response in the cell. Adapted from [101].

Figure 18

 18 Figure 18 Working principle and cellular response to the activation of the photosensitive Rac1 construct. (a) Graphic depiction of the optogenetic set-up used. Upon irradiation the LOV domain detaches from Rac1 triggering its activity. (b) Mutant Rac1 was obtained to diminish unwanted interactions with growth factors. (c) Light activation of a HeLa cell. (d) Localized photoactivation (red circle) evidencing the formation of ruffles and protrusions after repeated light pulses. Adapted from [104].

  Levskaya et al presented a light-switchable system based on the Phy-PIF interaction to induce translocation of the guanine nucleotide exchange factors (GEFs) responsible for the activation of the Rho-and Ras-family small G-proteins under study. Results demonstrated a global cell body contraction when triggering the recruitment of RhoGEF with light, and the possibility of inducing localized lamellipodia and actin assembly through the high spatiotemporal regulation in the activity of Rac and Cdc42, respectively[START_REF] Levskaya | Spatiotemporal Control of Cell Signalling Using A Light-Switchable Protein Interaction[END_REF].Having proven to be an important modulator of cell contractility and stress fibre formation, RhoA and its signalling pathway have been in the spotlight these last few years. Taking advantage of the precision and high specificity of the optogenetic approach, Rao et al used a LOV2 domain to photoactivate a downstream effector of the RhoA signalling pathway, a diaphanous related formin mDia1. This enabled a better characterization of this signalling domain showing its role in inducing filopodia, lamellipodia and F-actin formation, and uncoupling it from the cell contractile response[START_REF] Rao | An optogenetic tool for the activation of endogenous diaphanous-related formins induces thickening of stress fibers without an increase in contractility[END_REF].

Figure 19

 19 Figure 19 Working principle and cellular response to RhoA light activation. (A) Scheme showing the RhoA signalling cascade. (B) Cartoon depicting the activation of RhoA through the recruitment of GEF to the membrane using a TULIP optogenetic set-up. Images and quantification of the relative fluorescence intensity increase upon activation of GEF recruitment to the membrane (C-D), F-actin polymerization and reinforcement (E-F) and myosin accumulation (G-H). Scale bar, 10 μm. Adapted from [119].

Figure 20

 20 Figure 20 Modulation of cell contractility by optoGEF-RhoA translocation. (a-f) Clusters of cells expressing the optoGEF-RhoA construct and their response before and after photo-activation. (g, I, k) Mean traction profile of cells expressing optoGEF-RhoA that will translocate to the cell membrane upon light stimulation. Force peaks can be observed during light exposure. (h, j, l) Mean traction profile of cells expressing optoGEF-RhoA that will translocate to the mitochondria membrane upon light stimulation. Decrease of force can be observed during light exposure. Scale bar, 20 μm. Adapted from [121].

Figure 21

 21 Figure 21 Cell contractile responses to increasing sub-cellular RhoA activation areas. (a-b) Evolution of stained vinculin and traction forces in a cell before, during and after photo-activation. The orange box indicates the stimulated region. (c) Quantification of the strain energy and average number of focal adhesions in time before, during and after a period of light stimulation. (e) Traction force images showing the force increase with sequential number of photo-activations and augmenting light illuminated region (orange box). (f) Time plot of the experimental (black line) and theoretical (red line) contractile response to photo-stimulation in activation areas with increasing size. (g) Schematic of the biophysical model used to describe the cell behaviour. Scale bar, 10 μ m. Adapted from [43].

Figure 22

 22 Figure 22 The optogenetic system -CRY2/CIBN RhoA activation. (A) Scheme of the optogenetic system to trigger cell contractility. The system is based on overexpressing a RhoA activator (DHPH domain of ARHGEF11) fused to the light-sensitive protein CRY2-mcherry. The resulting protein is called optoGEF-RhoA. Upon illumination, CRY2 changes conformation and binds to its optogenetic partner

4

  years later by Lee et al who introduced a stretchable non-wrinkling film that incorporated beads as fiduciary markers of the film's reaction to cell traction forces (Fig. , giving birth to the technique known as Traction Force Microscopy (TFM) [125].

Figure 23

 23 Figure 23 Pioneer traction force microscopy experiments. (A) A fibroblast attached to a silicon rubber substrate that wrinkles under the exerted cellular force. (B) Graphic depiction of the nonwrinkling substrate. Small arrows represent the pulling forces exerted by the cell on the substrate and the long big arrow represents the direction of migration. (C) Phase contrast image showing a cell spread over the silicon substrate with latex beads embedded. Scale bar, 50 μm. Adapted from [124], [125].

Figure 24

 24 Figure[START_REF] Dorland | Cell-cell junctional mechanotransduction in endothelial remodeling[END_REF] Scheme of physiological tissue rigidity, from fat to cardiac muscle, compared to a rigid dish. Adapted from[START_REF] Kolahi | Effect of substrate stiffness on early mouse embryo development[END_REF].

  implement a home-made FTTC algorithm for our cell traction calculation. A MATLAB expert in our group, Irene Wang, developed a Fourier Transform Traction Cytometry software which combines Particle Image Velocimetry (PIV) and Particle tracking for displacement field measurements.

Figure 25

 25 Figure 25 Schematic diagram showing the displacement field determination by Particle Image Velocimetry and particle tracking. Adapted from [140].

Figure 26

 26 Figure 26 Classical traction force calculation on a single cell. (A) Brightfield image of a cell cultured on 5 kPa soft substrate (B) Image of the fluorescent beads embedded on the soft gel (C) Cell force map showing the calculated force arrow at each point plus the two main force axes (green and violet) and a reference line (red) (D) Cell stress map with colour bar showing the intensity of stress exerted by the cell (in Pa). Scale bar, 20 μm.

Figure 27

 27 Figure 27 Freely spread cells force dynamics upon photo-activation. (A) Quantification of the total force in time for cells expressing the optoGEF-RhoA construct. The light-blue discontinuous vertical line represents a light pulse of 100 ms exposure time at time=9.75 minutes. Each coloured curve

Figure 28

 28 Figure 28 Impact of different micropatterned geometries in the cellular actin skeleton and stress maps. (a) Top row: fluorescence fibronectin images of a non-patterned substrate and 3 different adhesive geometries. Bottom row: actin stained cells spread on the 4 different substrates (nonpatterned, Disk, Pac-man and bow). Scale bar, 10 μ m. (b) Representative image showing the overlap between the bead image before and after detaching the cell, evidencing the gel deformation.(c-d) Experimental and theoretical force traction fields, evidencing how the geometry of the adhesive fibronectin patterns induces a particular stress distribution. Adapted from[START_REF] Tseng | A new micropatterning method of soft substrates reveals that different tumorigenic signals can promote or reduce cell contraction levels[END_REF].

Figure 29 (

 29 Figure 29 (A) Micropatterns on acrylamide gel after detachment from the initially patterned surface. (B) Plot profile of ECM protein fluorescence measured along three micropatterns confirms the specificity of the coating, showing reproducible spacing between patterns and robust fluorescence intensity.

Figure 30

 30 Figure30Lamellipodia behaviour on micropatterned endothelial cells. Actin Fluorescence microscopy image of cells spread on 50 μm diameter circular micropattern (A) and on a 40μm x 40μm square adhesive geometry (B). DAPI stain in blue enables the visualization of the nuclei. Comparison in between both cases show that cell processes start preferentially from the corners. Adapted from[START_REF] Parker | Directional control of lamellipodia extension by constraining cell shape and orienting cell tractional forces[END_REF].

Figure 31

 31 Figure 31 Fibroblast constrained to a circular micropattern of 1000 um 2 adhesive area. (A) Disk shaped fibronectin micropattern on polyacrylamide hydrogels with 1000 um 2 surface area. (B) Individual actin-labelled cell. (C) Bright-field image merged with respective force maps and two main force cell axes. (D) Individual stress map calculated by Fourier Transform Traction Cytometry shows that traction forces are localized at cell contour. Both (C) and (D) show a bipolar force pattern.

Figure 32 Figure 33

 3233 Figure 32 Graphic depiction of the polarization degree. Values vary in between 0, where both main force axes are equal and isotropic, and 1, where all the cellular force is directed towards one axes implying maximum cell polarization.

Figure 34

 34 Figure 34 Time course of the strain energy and total force for cells spread on the disk-shaped micropattern. Full lines show mean values, shaded regions correspond to standard deviations. The curves represent averages of the reduced set of 23 circle-patterned cells and the duration of the experiment was of 52 minutes.

Figure 35 CRY2

 35 Figure35CRY2 membrane recruitment upon blue light (480 nm) activation. Fluorescence confocal microscopy images of a cell cultured on a disk-shaped adhesive island. During the "light-off" periods the CRY2-mCherry construct is cytoplasmic and this can be confirmed by an homogenous intensity with exception of the nucleus. When the blue light is switched on CRY2 translocates to the cell membrane where CIBN is anchored and this can be confirmed by an intensity increase at the cell edges.

BFigure 36

 36 Figure 36 Cell tensional response to repetitive or modulated light perturbations. Full lines show mean values, shaded regions correspond to standard deviations. The curves represent averages of the reduced set cells. Light blue dotted lines represent light activation events. (A) Quantification of the mean strain energy over 42 minutes for 7 cells on disk-shaped micropattern subjected to one 50 ms pulse of blue light followed by another one of the same exposure time 15 minutes later. (B) Quantification of the mean strain energy over 47 minutes for 12 cells on disk-shaped micropattern subjected to three pulses of increasing exposure time (10 ms, 20 ms , 50 ms) separated by a period of 10 minutes every time. Both graphs show clear tensional response upon light activation with a successive return to basal state.

  the 3 representative sizes can be observed along with the respective properly spread cell stained for actin. A plug-in from the image software Fiji, called OrientationJ, was used to qualitatively show the actin orientation of cells on the 3 sizes. A more detailed and quantified study of this orientation will be addressed further on. Stress maps of the 3 representative cells show qualitatively an increasing stress range. To characterize this trend in a more accurate way we performed live traction force measurements.

Figure 38 (

 38 Figure 38 (A) Disk shaped fibronectin micropatterns on polyacrylamide hydrogels with increasing surface area. The patterns cover an area of 500-1000-1500 μm 2 . (B) Fluorescence confocal microscopy images of individual actin-labelled cells. (C) Colour-coded map obtained with OrientationJ (plugin from Fiji) showing the orientation of actin fibres in the respective cells. (D) Individual stress maps calculated by Fourier Transform Traction Cytometry show that traction forces are localized at cell contour. (E) Bright-field images merged with respective force maps show that NIH 3T3 cells fully spread on all three patterns.

Figure 39

 39 Figure 39 Stable tensional levels displayed on cells of different sizes. (A) Time course of the strain energy for cells on the different disk sizes. Full lines show mean values, shaded regions correspond to standard deviations. Each curve represents averages of the reduced set of 8, 6 and 7 cells on 500, 1000, 1500 μm 2 respectively. Duration of the experiment was 56 minutes. (B) Static strain energy for cells spread on the three different disk sizes. A 1-way ANOVA test showed significant difference in between the three data groups.

Figure 40

 40 Figure 40 Larger cells produce higher strain energy both before and during activation. (A) Time course of the mean strain energy for cells on the different disk sizes subjected to one light pulse of 100 ms. Full lines show mean values, shaded regions correspond to standard deviations. Light blue dotted vertical light represents the photo-activation event. (B) Strain energy increase for every activated cell on the three different disks. A 1-way ANOVA test shows significant difference between the strain energy increase of cells on 500 μm 2 and the two bigger sizes. Each dot represents one cell.

Figure 41

 41 Figure 41 Larger cells display a higher actin arrangement. Quantification of the global cellular actin fibre alignment for cells spread on each disk size. Each dot represents one cell.

Figure 42

 42 Figure 42 Photo-activation does not induce actin re-arrangement. Time sequence of fluorescent microscope images of SiR actin stained cells on the three different disk adhesive geometries. At t=10 minutes cells were photo-activated with a pulse of blue light of 100 ms time exposure. Live actin images post-light activation, at t=15 minutes and t=20 minutes, do not show a change in the actin arrangement in any of the three sizes.

Figure 44

 44 Figure 44 Quantification of the order parameter of cells on 10 different micropatterns. Each dot represents one cell and each data set corresponds to cells cultured on the micropattern depicted directly above, at the top of the graph.

Figure 45

 45 Figure 45 Time course actin organization for cells on wheel. Fluorescence confocal images of a SiRactin stained cell spread on a Wheel pattern. Pictures were taken every 10 minutes for a total experimental time of 10 hours.

8 AFigure 46

 846 Figure 46 Cells on Wheel present a lower actin alignment than those on Disk. (A) Order parameter quantification for cells spread on Disk (blue) and Wheel (red). Each dot represents one cell. (B) Qualitative comparative analysis between cells on both shapes showing the fibronectin patterns on polyacrylamide gels, fluorescence confocal images of individual actin-labelled cells and actin images analysed with OrientationJ (Fiji plugin).

CFigure 47

 47 Figure 47 Similar tensional level for cells on Disk vs cells on Wheel. (A) Qualitative comparison between a representative cell on Disk and another on Wheel. From left to right and then inverted: Fluorescence confocal microscopy images of individual actin-labelled cells. Disk/Wheel shaped fibronectin micropatterns on polyacrylamide hydrogels. Both patterns cover an area of 1000 μm 2 . Individual stress maps calculated by Fourier Transform Traction Cytometry show a tripolar force pattern for the Wheel and a more bipolar one for the Disk. (B) Time course of the strain energy for cells on the two different patterns. Full lines show mean values, shaded regions correspond to standard deviations. Each curve represents averages of the reduced set of 23 cells. Duration of the experiment was 52 minutes. (C) Static strain energy for cells spread on the Disk and the Wheel shape. Using a nonparametric t-test, significant difference is not found between the two cases.

Figure 48

 48 Figure 48 Higher contractile response obtained for cells on Disk against Wheel. (A) Normalized quantification of the mean strain energy over time for cells on both shapes subjected to one light pulse of 100 ms. Full lines show mean values, shaded regions correspond to standard deviations. Each curve represents averages of the reduced set of 7 cells. Duration of the experiment was 22 minutes. (B)Strain energy increase for every activated cell on the two different shapes. Calculation is made by subtracting the strain energy value before activation to the highest strain energy value obtained after light activation. A non-parametric t-test showed significant difference in between both data sets.

Figure 49

 49 Figure 49 Effective physical representation of the cell and the elastic substrate on different fibronectin patterns and qualitative distribution of simulated traction stresses contrasted with experimental ones. (A) A Kelvin-Voigt model with active contractility and coupling to an elastic foundation is used to reconstruct the dynamic energy response of cells upon global optogenetic activation (side view). (B) From top to bottom: Distribution of the spring stiffness, experimental stress maps obtained during photo-activation and a typical qualitative stress map during the simulated photo-activation of Disk-patterned and Wheel-patterned cells, respectively.

Figure 50 A

 50 Figure 50 A representative cell spread on the Ring shape. From left to right: 1000 μm 2 ring shaped fibronectin micropattern on polyacrylamide hydrogels. Individual actin-labelled cell. Colour-coded map obtained with OrientationJ (plugin for Fiji) showing the orientation of actin fibres in the cell. Brightfield image merged with respective force map. Individual stress map calculated by Fourier Transform Traction Cytometry, showing dipolar force traction similar to that one seen for cells on the Disk.

Figure 51

 51 Figure 51 Cells on the Ring display a similar order parameter than that of the Disk. Order parameter quantification for cells spread on Disk (blue), Ring (Pink) and Wheel (red). Each dot represents one cell. A 1-way ANOVA test showed significant difference in between cells spread on Wheel and those on Disk and Ring, but no significant difference between Ring and Disk.

CFigure 52

 52 Figure 52 Similar contractile response obtained for cells on Disk and Ring. (A) Normalized quantification of the mean strain energy over time for cells on the three shapes subjected to one light pulse of 100 ms time exposure. Full lines show mean values, shaded regions correspond to standard error of the mean. Duration of the experiment was 22 minutes. Light-blue dashed vertical light marks the photo-activation event. (B) Strain energy increase for every activated cell on the three different shapes.Calculation is made by subtracting the strain energy value before activation to the highest strain energy value obtained after light activation. A 1-way ANOVA test showed a significant difference in between the Wheel and both the Ring and the Disk. No significant difference was seen between Ring and Disk.

Figure 53

 53 Figure 53 Similar focal adhesion characteristics for cells spread on Ring, Disk and Wheel. (A) Disk, Ring and Wheel fibronectin patterns on polyacrylamide hydrogels. (B) Individual vinculin-stained cells.

± 20 . 5 BFigure 54

 20554 Figure 54 Plot showing focal adhesion characteristics for cells spread on Ring, Disk and Wheel. (A-B) Quantification of the total area covered by the focal adhesions, and average area of individual focal adhesions on each pattern. Each dot represents a cell. Disk (N=69), Ring (N=43) and Wheel (N=41).

Figure 55

 55 Figure 55 Effect of the cellular area on the strain energy level as well as its energy gain and dynamics upon photoactivation of increasing duration. Full lines show mean values, shaded regions correspond to standard error of the mean. Each curve corresponds to an average of 9, 11, and 11 cells for 500 μm 2 , 1000 μm 2 and 1500 μm 2 circular adhesive micropatterns, respectively. The activation pulses (represented by light-blue vertical discontinuous lines) were of 10, 20, 50, 100, 150 and 200 ms duration.

7 Figure 56

 756 Figure 56 Effect of the actin alignment on the normalized energy gain and dynamics upon photoactivation of increasing duration. Full lines show mean values, shaded regions correspond to standard error of the mean. Each curve corresponds to an average of 7 cells both for the Disk and the Wheel micropatterns. The activation pulses (represented by light-blue vertical discontinuous lines) were of 10, 20, 50, 100, 150 and 200 ms duration.

Figure 57

 57 Figure 57 Stress dynamics as a function of the photo-activation duration. (A) Stress increase versus photo-activation duration for cells on Disk and Wheel showing a saturation point after 100 ms exposure time. Dots represent experimental values and full lines were obtained with the biophysical model. A higher strain response can also be observed for the cells on the Disk all along the optoprotocol. (B) Stress activation (full dots) and relaxation (crosses) times versus photo-stimulation exposure times. (C) Stress activation (full dots) and relaxation (crosses) constants versus photostimulation exposure times. Both activation times and constants are independent of the PA duration. Relaxation times and constant increase in a saturating manner as a function of the PA duration, i.e. a longer PA duration has a longer impact on the contractility of cells. Grey dots and crosses correspond to the Disk pattern, while blue dots and crosses refer to the Wheel pattern.

  This technique allows rapid light-mediated protein activation, with the added advantages of low toxicity and reversibility. Although originally developed for neuroscience, where ion channels or ion transporters are activated by light, during recent years it has been also increasingly applied to the cytoskeleton, where light-sensitive domains are used to effect an allosteric change in a protein of interest (Weitzman & Hahn, 2014; Tischer & Weiner, 2014; De Renzis review Trends in Cell Biology 2016).

  Edwards and Schwarz PRL 2011, Mertz et al. PRL 2012, Oakes Geometry Regulates Traction Stresses in Adherent Cells BPJ 2014). This model describes the cell as a Kelvin-Voigt solid with isotropic active stresses and an elastic foundation. Using traction force microscopy, we first quantified the forces and strain energies exerted by single opto-3T3 fibroblasts spread on disc shaped fibronectin micropatterns printed on soft (5kPa) polyacrylamide hydrogels of increasing areas (500, 1000, 1500 m 2 ) (Figure 1a). Cell strain energy increases as a function of cell spreading area (Figure 1c), as previously described by other studies [Tan-Chen PNAS 2003; Reinhart-King-Hammer BiophysJ 2005;

Figure 1 :

 1 Figure 1: Larger cells display a higher strain energy production in response to transient RhoA perturbations (a) Disk shaped fibronectin micropatterns on polyacrylamide hydrogels with increasing surface area. The patterns cover an area of 500-1000-1500 um2. (b) Individual actin-labelled cells. (c) Bright-field images merged with respective force maps. They show that NIH 3T3 cells fully spread on all three patterns. (d) Individual stress maps calculated by Fourier Transform Traction Cytometry show that traction forces are localized at cell contour. (e) Static strain energy for cells spread on the three different disk sizes. Using a 1-way ANOVA test, significant difference is found between cells spread on 500 um2 pattern and the other two bigger sizes. (f) Global cellular actin fibre alignment for cells spread on each disk size. This is represented by the actin order parameter. (g) Quantification of the mean strain energy over time for cells on the different disk sizes subjected to one light pulse of 100 ms. (h) Strain energy increase for every activated cell on the three different disk sizes.Calculation is made by subtracting the strain energy value before activation to the highest strain energy value obtained after light activation.

Figure 2

 2 Figure 2 Actin organization regulates the cell's contractile efficiency. From left to right: 1000 um2 disk shaped and hazard shaped fibronectin micropatterns on polyacrylamide hydrogels with increasing surface area (both patterns cover the same projected area). Colour-coded map given by OrientationJ (plugin for Fiji) showing the angle of oriented features in the image. Individual actin-labelled cells. Bright-field images merged with respective force maps. Individual stress maps calculated by Fourier Transform Traction Cytometry. (b) Static strain energy for cells spread on the 1000 um2 disk and the hazard

  From my point of view, and based on what I presented in this work, tensional homeostasis is the correct way to address it. As a future perspective, I would set the focus of the research on the previously mentioned feedback loops, both the positive and the negative ones, and how neighbouring cells impact on them. Most of the work already done has targeted positive feedback loops by imposing 'positive' perturbations, inducing the cell to readjust the system by reducing the momentary tensional increase. Valon et al have recently used an optogenetic construct to downregulate the activity of RhoA [121]. Probing negative feedback loops, as the one just mentioned, might bring exciting insights and better contribute to our understanding of the cellular tensional balance.

  homeostasis in single cells. Derived from the general concept of homeostasis: an elemental adaptive biological process that is of vital importance in maintaining whole-cell/tissue physiology against external perturbations; this tensional by-product is the cellular homeostasis to mechanical perturbations. To study this phenomenon we used an engineered fibroblast cell line carrying a CRY2/CIBN light-gated dimerizer system coupled to a RhoA activator ARHGEF11. This optogenetic approach allowed us to perturb the global cellular contractile state through the activation of the RhoA signaling cascade with high spatio-temporal resolution. In a reliable and reproducible fashion we were able to study the stress energy increases of the cell to light pulses of varying intensities. The force and contractile readouts were obtained by using a Traction Force Microscopy (TFM), a standard method to study the cellular traction forces produced by stationary or migrating cells on elastic substrates. Finally, in order to constrain the cell so as to avoid migration, analyse contractile responses on different cell sizes and actin network arrangement, and narrow down variables we included the micropatterning technique in our experimental set-up.All the work done during this project significantly increased my understanding of optogenetic techniques and cellular force measurements, giving me a thorough introduction to the field of mechanobiology. Moreover, on the experimental side, I gained huge expertise in soft substrate engineering and live cell experimentation.Results obtained all along the thesis taught me many interesting things. Starting from a general point of view, they reinstated the inherent variability of biological systems and the difficulty and complexity of classifying cellular mechanical behaviours within a defined range of values, hence the necessity of a critical spirit at the moment of evaluation.

Figure 58 (

 58 Figure 58 (A) Scheme of cells plated on the gel (left), and cell detached from the gel after trypsination (right). (B) ''before kill'' and ''after kill'' microscopy fluorescence images. (C) Composite image of the BK and AK images, with a close-up clearly showing the displacement of beads as a consequence of the deformation of the gel done by the cell. Scale bar, 15 μ m.

  Webster et al.'s work:"This behaviour (the non-returning to original steady-state) is in contrast to the strict definition of tensional homeostasis that predicts a fixed contractile setpoint…" Such remark puts in evidence how the concept of tensional homeostasis has received different interpretations since it was coined in 1998. At that time, Brown et al presented it as a control mechanism that would, based on the environment, keep a certain level of tension in the cell against external mechanical variations. For some, this certain level has meant a dynamic range and for others a more specific value.

Acknowledgements

Summary

Pulling together the techniques described in this Chapter, we developed a unique tool coupling a CRY2/CIBN optogenetic system with patterned traction cytometry. Such a set-up would enable us to apply global internal perturbations to living single cells via reproducible and highly controlled pulses of blue light (460 nm), while acquiring traction force cellular responses with a subcellular resolution in real time.

Leveraging the unique capability of systematically activating the endogenous level of RhoA, we can successfully characterize the dynamic cell contractile response by triggering the RhoA signaling pathway in a controlled manner with high spatiotemporal resolution. Moreover, the addition of geometrical constraints, through the use of micropatterns, enables the control of actomyosin organization, enabling a deeper understanding of its role in dynamical tensional homeostasis. light exposure time (Fig. 37), we find the same positive correlation between the light exposure and the cellular contractile response.

Figure 37 Membrane recruitment of the CRY2/CIBN system upon increasing time exposure light activations. Quantification of fluorescence increase in the same cell, with a light exposure variation from 3 to 200 ms, and constant laser power. Adapted from [123].

. In a more detailed analysis of the graphs in figure 36, it can be seen that a light pulse of 50 ms time exposure induced an averaged cellular contractile energy maximum increase of 3.20456E-13 ± 1.34598E-13 J in 2.025 ± 0.56 minutes. The relaxation time of the system to the basal tensional state was 8.61 ± 1.82 minutes. For 20 ms light pulse the maximum stress amplitude 1.28448E-13 ± 9.10807E-14 J was achieved in 1.73 ± 0.41 minutes with a return to equilibrium in 3.44 ± 0.74 minutes. Finally, a light pulse of 10 ms exposure time induced a contractile maximum increase of 4.51817E-14 ± 4.01348E-14 J in 1.42 ± 0.42 minutes with a time relaxation of 2.54 ± 1.15 min. This results seem to imply a correlation in between the amount of light used and the cell's tensional response, both in amplitude and time.

Having confirmed the tensional homeostatic behavior in constrained single cells and characterized the probing system we can move on to the more detailed analysis and interrogation of the cellular dynamical contractile responses. same projected area (1000 μm 2 ) and shape (circular) on spread cells but offered different sub-cellular geometries or boundary adhesiveness. The common saturation point discussed earlier would be implying a fascinating fact: the highest contractile point that a cell spread on any of the studied micropatterns could reach upon photo-activation did not depend on its size or its internal actin arrangement. Consequently, the reason for this saturation could be linked to a saturated myosin capacity or a RhoA activity limit. Deeper understanding and characterisation of this force response saturation could be addressed in further research projects.

Manuscript (unfinished version)

Actin architecture and biochemical activation control single cell tension setpoint

Andersen T 1 , Probst D 2 , Wang I 1 , Moreau P 1 , Fitzpatrick V, Boudou T 1 , Schwarz U 2 *, Balland M 1 * 1 Laboratoire Interdisciplinaire de Physique, Grenoble Alpes University, Saint Martin d'Hères, France Like for many other physiological processes, it has been suggested that cells maintain a characteristic setpoint in tension, so that they can adapt to their mechanical environment (tensional homeostasis).

Here we test this hypothesis combining recent advances in traction force microscopy on soft elastic substrates, micropatterning and optogenetics. We find that after transient whole-cell Rho-activation achieved by a Cry2/CBAN-construct, cells return to a constant tension setpoint with near perfect precision. However, we also find that this setpoint is variable, increasing not only with cell spread area, but also with the actin order parameter. Fitting the experimental traction force data to a theoretical model for active contractile systems reveals that force transmission to the environment is reduced when different actin orientations work against each other in the same cell. The peak values for the activation stresses saturate with increasing activation time at a value around 100 ms and are largest for completely polarized cells. Together, our results show that single cells do maintain internal setpoints for tension, which however are constrained by actin architecture and biochemical activation.

Cell culture and plating

Stable cell line NIH 3T3 fibroblasts with CIBN-GFP-CAAX and optoGEF-RhoA constructs (kindly provided by L. Valon and M. Copper, Institute Curie, Paris, France) were cultured in Dulbecco's Modified Essential Medium (DMEM) containing 10% foetal bovine serum (FBS) and 0.2% penicillinstreptomycin. Cells were grown in a humidified 5% CO2 incubator at 37ºC. Cells were seeded on patterned substrates at a density of 200.000cells/cm3. All traction force measurements or immunostainings were performed 4 hours after seeding to ensure full spreading of the cells.

Leibovitz's L-15 medium, supplemented with 10% FBS and 0.2% penicillin-streptomycin, was used as imaging media for every live imaging experiment.

Live cell imaging and activation

Cell imaging and activation intended for posterior force measurements was carried out using a Nikon Ti-E microscope, Zyla sCMOS camera (Andor, Belfast, UK) and Plan Apo VC 60x/1.40 Oil objective (Nikon). The microscope was equipped with an incubator that maintains the temperature at 37 °C.

Global cellular photoactivation was performed using a LED light source (X-Cite/XLED1, Lumen Dynamics, Canada) coupled to a Mosaic digital micromirror device (Andor). Depending on the experiment done, activation pulses were 10-20-50-100-150-200 ms long using an LED at 460 nm with power of 256.7 uW (measured at the back focal plane of the objective).

Cell stainings

For stress fibre labelling, cells were permeabilized and fixed for 10 min with 0.2% W/V Triton X-100 and 4% paraformaldehyde in DPBS buffer to preserve cell shape. Fixed samples were washed with PBS and incubated in blocking buffer for 45 min. Afterwards, cells were stained with phalloidin at 1 mM (Sigma-Aldrich) for 1 hour and finally mounted on glass slides with Mowiol 4-88 (Polysciences, Inc.) and kept at 4ºC overnight.

For live actin measurements, cells were incubated overnight in DMEM medium supplemented with 100 nM SiR-actin (SPIROCHROME) and 10 M verapamil.

Both live and fixed actin imaging was carried out with a Leica TCS SPE confocal microscope with an HCX PL APO 63x/1.40 oil objective. The microscope was controlled through the Leica Application Suite (LAS) X software. Pictures were then processed using Fiji software.

Actin order parameter analysis

This parameter was obtained with a program that calculates the local orientation in actin images using the structure tensor. The program will first smooth the original image using a Gaussian filter.

Then, based on the intensity level, the region in the cell is segmented.

Appendix A -Materials and Methods

Polyacrylamide hydrogel micropatterning -Mask method

Description of the procedure based on the work done by Vignaud, Hajer Ennomani, and [START_REF] Vignaud | Polyacrylamide Hydrogel Micropatterning[END_REF] with modifications done at Motiv group [START_REF] Vignaud | Polyacrylamide Hydrogel Micropatterning[END_REF].

Coverslip silanization • This glass treatment is necessary to ensure a good attachment between the PAA gel and the underlying coverslip.

• As silane solutions are toxic, this process should be performed under a chemical hood with appropriate user protection, the silane solution should not leave the hood outside of a hermetically closed container.

• Mix in a 15 ml falcon: 5ml of 100% alcohol, 161ul of 10% acetic acid and 18,5ul bind silane (Plusone Bind-Silane, Silane A-174, M.W. 248.35 g/mol).

• Put 100-200ul of silane solution on each coverslip. • After 3-4 minutes wipe each coverslip with a kimwipe. (Do not let the coverslip dry before wiping it).

• Leave for 10 minutes to make sure the coverslips are dry and store them at room temperature in a petri dish. Seal the petri dish with parafilm to avoid air dust from getting in. •This treatment is quite stable over few weeks so you can do many coverslips at the same time to avoid always repeating this fastidious time-consuming process.

pLL-PEG solution preparation

• This solution will be used for the passivation of coverslips before UV exposure and protein coating to avoid unspecific adsorption of protein outside of the exposed area.

• pLL-PEG is usually received as powder and should be stored under protective atmosphere (Argon) if possible, at 20° C. The final concentration we want to achieve is 0.1 mg/ml. Since the powder is usually made of grains that weigh a few mg each, we first produce 1 mg/mL solution that is aliquoted and stored at 20° C. The final solution will be diluted from stock.

• Prepare HEPES 10 mM from powder and milliQ water.

• Equilibrate the pH of the HEPES solution to 7.4 using NaOH.

• Weigh the pLL-PEG and add corresponding HEPES volume to reach a final concentration of 1 mg/mL. Then filter the solution using a syringe and a filter of 0.22 mm mesh size. Aliquot the solution and store at 20° C. • When needed, thaw an aliquot and dilute it 10 times in HEPES solution to achieve a 0.1 mg/mL pLL-PEG concentration. The pLL-PEG solution should be then stored at 4° C and used within few days.

Preparation of acrylamide solution and polymerization reagent • Again, as acrylamide is carcinogenic, handle it with care under chemical hood and using proper user protection.

• To know the proportions required for a specific desired final gel rigidity, one can use the table from Tse and Engler (2001) which covers a wide range of rigidities.

• Mix acrylamide and bis-acrylamide solution in PBS to obtain the desired concentration.

• This solution can be stored for a couple of months at 4° C.

• TEMED solution was used as received without further preparation.

• APS solution was prepared from powder in water milliQ at a concentration of 10% w/w and immediately frozen in small 10 mL aliquots and stored at 20° C.

Cell stainings

For stress fibre labelling, cells were permeabilized and fixed for 10 min with 0.2% W/V Triton X-100 and 4% paraformaldehyde in DPBS buffer to preserve cell shape. Fixed samples were washed with PBS and incubated in blocking buffer for 45 min. Afterwards, cells were stained with phalloidin at 1 mM (Sigma-Aldrich) for 1 hour and finally mounted on glass slides with Mowiol 4-88 (Polysciences, Inc.) and kept at 4 ºC overnight.

For live actin measurements, cells were incubated overnight in DMEM medium supplemented with 100 nM SiR-actin (SPIROCHROME) and 10 M verapamil.

Both live and fixed actin imaging was carried out with a Leica TCS SPE confocal microscope with an HCX PL APO 63x/1.40 oil objective. The microscope was controlled through the Leica Application Suite (LAS) X software. Pictures were then processed using Fiji software.

Actin order parameter analysis

This parameter was obtained with a program that calculates the local orientation in actin images using the structure tensor. The program will first smooth the original image using a Gaussian filter. Then, based on the intensity level, the region in the cell is segmented.

For each pixel in the cell, the structure tensor J (that has 3 elements: J11, J12 and J22) is computed in a local neighbourhood that is also Gaussian. The orientation angle, the coherency and a measure of local gradient (gray level is constant or it changes) are computed from the elements of the structure tensor (λi are the eigenvalues of J):

The average orientation and order parameter S will be computed by averaging over all pixels for which the coherency is above a threshold value, which can be changed. Average angle: θm=〈θ〉c>thres Order parameter: S=〈cos(2(θ-θm))〉c>thres (S=1 means that the local orientation is parallel to the average orientation, S=0 means that they are orthogonal).

Vinculin staining

After 4 h of culture on the micropatterns, cells were fixed with 3.7% formaldehyde in PBS, permeabilized with 0.2% Triton X-100 in TBS (50 mM Tris-HCl, 0.15 M NaCl, pH 7.4) and blocked with 2% BSA (Sigma Aldrich) in TBS. The samples were then incubated with primary antibodies against vinculin (Sigma Aldrich) and detected with Alexa 488-conjugated, isotype-specific, anti-IgG antibodies (Invitrogen). Actin was labeled with phalloidin-TRITC (Sigma) and nuclei were stained with DAPI (Life Technologies).

Areas of focal adhesions were segmented and measured by using a home-made Image J (National Institutes of Health) routine. fluorescent pictures were taken of the coordinates where the cells were. In Figure 59 it can be clearly seen how forces exerted by the cell deform the ECM geometries on which they are plated.

The physical role of the nucleus

As it was mentioned during Chapter 1, the nucleus is amongst the most important elements of the cellular mechanosensing machinery. It not only regulates cellular physical behaviour through gene expression, but it is also physically connected to the actomyosin network and the cytoskeleton through the LINC (Linker of Nucleoskeleton and Cytoskeleton) complex [START_REF] Crisp | Coupling of the nucleus and cytoplasm: Role of the LINC complex[END_REF], thus playing also a mechanical role in the cellular mechanoresponses (Fig. 60).

Several studies have been carried out to clarify how DNA replication, gene regulation and molecular pathways triggered by the nuclear lamina impact on the cellular mechanotransduction [START_REF] Wang | Mechanotransduction at a distance: Mechanically coupling the extracellular matrix with the nucleus[END_REF], [START_REF] Metzger | MAP and kinesin-dependent nuclear positioning is required for skeletal muscle function[END_REF]- [START_REF] Graham | Mechanotransduction and nuclear function[END_REF].

However, not much is known when it comes to identifying how important is, for the cell, the nucleus physical presence at the moment of regulating cell polarity, migration and tensional homeostasis. For this reason, the following study focused on studying these processes in the absence of the nucleus. Using enucleated cells and knock-out cell lines, Graham et al. studied the onset of cellular polarization and migration in 1D, 2D and 3D environments and on substrates with varying rigidities.

Appendix C -Biophysical model to predict the experimental data