Living cells sense the rigidity of their environment and adapt their activity to it. In particular, cells cultured on elastic substrates align their shape and their traction forces along the direction of highest stiffness and preferably migrate towards stiffer regions. Although numerous studies investigated the role of adhesion complexes in rigidity sensing, less is known about the specific contribution of acto-myosin based contractility. Here we used a custom-made single-cell technique to measure the traction force as well as the speed of shortening of isolated myoblasts deflecting microplates of variable stiffness. The rate of force generation increased with increasing stiffness and followed a Hill force-velocity relationship. Hence, cell response to stiffness was similar to muscle adaptation to load, reflecting the force-dependent kinetics of myosin binding to actin. These results reveal an unexpected mechanism of rigidity sensing, whereby the contractile acto-myosin units themselves can act as sensors. This mechanism may translate anisotropy in substrate rigidity into anisotropy in cytoskeletal tension, and could thus coordinate local activity of adhesion complexes and guide cell migration along rigidity gradients.mechanosensing | adaptation to load | cell migration | cell spreading | cell mechanics A s part of their normal physiological functions, most cells in the organism need to respond to mechanical stimuli such as deformations, forces, and the geometry and stiffness of the extracellular matrix (1, 2). Aberrant mechanical responsiveness is often associated with severe diseases, including cardiovascular disorders, asthma, fibrotic diseases, or cancer metastasis.Since the early 1980s, several techniques have been developed to characterize the forces generated by living cells (3-5) and to investigate the effect of the mechanical properties of twodimensional (2D) substrates (6-8). It was shown that cells are able to sense and respond to the rigidity of their surroundings. For instance, cells cultured on elastic substrates with a rigidity gradient preferably locomote towards stiffer regions and align their shape, their cytoskeletal structures, and their traction forces along the direction of highest stiffness (9-11). Moreover, it has been demonstrated that matrix rigidity could direct stem cells' lineage specification (12).It is generally assumed that rigidity sensing is based on mechanochemical signal-transduction pathways. The search for the mechanosensing element has generated numerous plausible candidates (reviewed in ref.2). The most prominent of them is the focal adhesion complex (13,14). These molecular assemblies consist of numerous proteins that are associated with integrin adhesion receptors (15) and provide the pathway of force transmission from the cytoskeleton to the extracellular matrix (16). Adhesion of integrins to extracellular matrix proteins triggers the formation of focal adhesions, their connection to actin, and the contraction of the cytoskeleton by myosin II (17-19). On a soft substrat...

Epithelial monolayers are one-cell thick tissue sheets that separate internal and external environments. As part of their function, they have to withstand extrinsic mechanical stresses applied at high strain rates. However, little is known about how monolayers respond to mechanical deformations. Here, by subjecting suspended epithelial monolayers to stretch, we find that they dissipate stresses on a minute timescale in a process that involves an increase in monolayer length, pointing to active remodelling of cell architecture during relaxation. Strikingly, monolayers consisting of tens of thousands of cells relax stress with similar dynamics to single rounded cells and both respond similarly to perturbations of actomyosin. By contrast, cell-cell junctional complexes and intermediate filaments do not relax tissue stress, but form stable connections between cells, allowing monolayers to behave rheologically as single cells. Taken together our data show that actomyosin dynamics governs the rheological properties of epithelial monolayers, dissipating applied stresses, and enabling changes in monolayer length. the Rosetrees Trust, the UCL Graduate School, the EPSRC funded doctoral training program CoMPLEX, and the European Research Council (ERC-CoG MolCellTissMech, agreement 647186 to GC). N.K. was in receipt of a UCL Overseas Research Scholarship. N.K. was supported by the Prof Rob Seymour Travel Bursary Fund for research visits to Barcelona. J.F. and A.B. were funded by BBSRC grant (BB/M003280 and BB/M002578) to G.

Living cells adapt to the stiffness of their environment. However, cell response to stiffness is mainly thought to be initiated by the deformation of adhesion complexes under applied force. In order to determine whether cell response was triggered by stiffness or force, we have developed a unique method allowing us to tune, in real time, the effective stiffness experienced by a single living cell in a uniaxial traction geometry. In these conditions, the rate of traction force buildup dF∕dt was adapted to stiffness in less than 0.1 s. This integrated fast response was unambiguously triggered by stiffness, and not by force. It suggests that early cell response could be mechanical in nature. In fact, local force-dependent signaling through adhesion complexes could be triggered and coordinated by the instantaneous cell-scale adaptation of dF∕dt to stiffness. Remarkably, the effective stiffness method presented here can be implemented on any mechanical setup. Thus, beyond single-cell mechanosensing, this method should be useful to determine the role of rigidity in many fundamental phenomena such as morphogenesis and development.cell mechanics | mechanotransduction | dynamic stiffness control L iving cells are sensitive to their mechanical environment and adapt their activity to it. Many parameters such as forces, deformations, and the geometry and stiffness of the ECM were identified that could trigger cellular functions (1-3). In particular, it was shown that the stiffness of the ECM could influence cell spreading (4, 5), orientation (6), contractility (7,8), migration (9), and even differentiation (10, 11). These phenomena were mainly attributed to the ability of adhesion complexes to respond to applied forces (12, 13). These complexes, based on integrin transmembrane proteins, transmit forces from inside (cytoskeleton) to outside the cell (ECM) (14, 15) and were thus natural candidates for mechanosensing. On soft substrates, cell contractility could induce high substrate deformation and low generated forces. The adhesion complexes would then be weakly deformed, leading to a weak cell response. On stiff-less deformablesubstrates, cell contractility could lead to high stretching of mechanosensory molecules that would activate specific mechanochemical signaling pathways and enhance, in turn, contractility (9,16,17).Following the observation that nonmuscle myosins were needed for stem cells to feel matrix elasticity (11), we have recently investigated the specific role of actomyosin contractility in rigidity sensing. We found that cell response to the rigidity of its environment could reflect the adaptation of the actomyosin machinery to load (8). In this context, it is noteworthy that mechanosensing through adhesion-based signaling pathways and actomyosin-based sensitivity should lead to cell responses occurring at distinct characteristic time scales. At short times, an "instantaneous" actomyosin-dependent response could adapt the cytoskeletal tension, followed, at longer times, by the onset of the regulatory adhesio...

Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodeling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger an intrinsic mechanical response of the actomyosin cortex. Cortical retrograde flow resulting from actin polymerization at the edges is shown to be modulated by the stress resulting from myosin contractility, which in turn, regulates the cell length in a forcedependent manner. The model describes the maximum force that cells can exert and the maximum speed at which they can contract, which are measured experimentally. These limiting cases are found to be associated with energy dissipation phenomena, which are of the same nature as those taking place during the contraction of a whole muscle. This similarity explains the fact that single nonmuscle cell and wholemuscle contraction both follow a Hill-like force-velocity relationship. -5). This behavior is strongly dependent on the contractile activity of the actomyosin network (6-10). One of the cues driving the cell response to its environment is rigidity (11). Cells are able to sense not only the local rigidity of the material with which they are in contact (12) but also, the one associated with distant cell substrate contacts. This ability has been demonstrated by tracking the amount of extra force needed to achieve a given displacement of microplates between which the cell is placed (13, 14) (Fig. 1B), of an atomic force microscope (AFM) cantilever (15, 16) or elastic micropillars (17). This cell-scale rigidity sensing is totally dependent on myosin-II activity (13). A working model of the molecular mechanisms at play in the actomyosin cortex is available (18), where myosin contraction, actin treadmilling, and actin cross-linker turnover are the main ingredients. Phenomenological models (19, 20) of mechanosensing have been proposed but could not bridge the gap between the molecular microstructure and this cell-scale phenomenology. Here, we show that the collective dynamics of actin, actin cross-linkers, and myosin molecular motors are sufficient to explain cellscale rigidity sensing: depending on the tension that can be borne by the environment, there is a change of the fraction of myosin molecules which perform mechanical work that is effectively transmitted rather than dissipated. The model derivation is analogous to the one of rubber elasticity of transiently cross-linked networks (21), with the addition of active crosslinkers accounting for the myosin. It involves four parameters only: myosin contractile stress, speed of actin treadmilling, elastic modulus, and viscoela...

Structural properties of articular cartilage such as proteoglycan content, collagen content and collagen alignment are known to vary over length

The mechanical response of single cells and tissues exhibits a broad distribution of time-scales that often gives rise to a distinctive power-law rheology. Such complex behaviour cannot be easily captured by traditional rheological approaches, making material characterisation and predictive modelling very challenging. Here, we present a novel model combining conventional viscoelastic elements with fractional calculus that successfully captures the macroscopic relaxation response of epithelial monolayers. The parameters extracted from the fitting of the relaxation modulus allow prediction of the response of the same material to slow stretch and creep, indicating that the model captured intrinsic material properties. Two characteristic times, derived from the model parameters, delimit different regimes in the materials response. We compared the response of tissues with the behaviour of single cells as well as intra and extra-cellular components, and linked the power-law behaviour of the epithelium to the dynamics of the cell cortex. Such a unified model for the mechanical response of biological materials provides a novel and robust mathematical approach to consistently analyse experimental data and uncover similarities and differences in reported behaviour across experimental methods and research groups. It also sets the foundations for more accurate computational models of tissue mechanics.

Throughout embryonic development and adult life, epithelia are subjected to compressive deformations. While these have been shown to trigger mechanosensitive responses such as cell extrusion and differentiation, which span tens of minutes, little is known about how epithelia adapt to compression over shorter timescales. Here, using suspended epithelia, we uncover the immediate response of epithelial tissues to the application of in-plane compressive strains (5-80%). We show that fast compression induces tissue buckling followed by actomyosin-dependent tissue flattening which erases the buckle within tens of seconds, in both mono-and multi-layered epithelia. Strikingly, we identify a well-defined limit to this response, so that stable folds form in the tissue when compressive strains exceed a 'buckling threshold' of ~35%. A combination of experiment and modelling shows that this behaviour is orchestrated by adaptation of the actomyosin cytoskeleton as it re-establishes tissue tension following compression. Thus, tissue pre-tension allows epithelia to both buffer against deformation and sets their ability to form and retain folds during morphogenesis.

Cell shape affects proliferation and differentiation, which are processes known to depend on integrin-based focal adhesion (FA) signaling. Because shape results from force balance and FAs are mechanosensitive complexes transmitting tension from the cell structure to its mechanical environment, we investigated the interplay between 3D cell shape, traction forces generated through the cell body, and FA growth during early spreading. Combining measurements of cell-scale normal traction forces with FA monitoring, we show that the cell body contact angle controls the onset of force generation and, subsequently, the initiation of FA growth at the leading edge of the lamella. This suggests that, when the cell body switches from convex to concave, tension in the apical cortex is transmitted to the lamella where force-sensitive FAs start to grow. Along this line, increasing the stiffness resisting cell body contraction led to a decrease of the lag time between force generation and FA growth, indicating mechanical continuity of the cell structure and force transmission from the cell body to the leading edge. Remarkably, the overall normal force per unit area of FA increased with stiffness, and its values were similar to those reported for local tangential forces acting on individual FAs. These results reveal how the 3D cell shape feeds back on its internal organization and how it may control cell fate through FA-based signaling.mechanosensing | cell spreading | cortical tension | cell mechanics W hen cells are cultured on flat substrates, their functions and fate can be modulated by the size and shape of the surface they are allowed to spread on (1-6). In particular, the cell spread area was shown to control the balance between proliferation and apoptosis (1), DNA synthesis (3), and histone acetylation (6). Although the mechanisms behind these phenomena remain to be defined, focal adhesions (FAs) and actomyosin-dependent contractility are clearly involved. For instance, constitutively active focal adhesion kinase (FAK) restores proliferation in nonadherent cells (7,8). Indeed, FAs are assemblies of multiple proteins among which many are part of fundamental networks of regulation of cell functions (9, 10). Moreover, FAs are mechanosensitive anchors that resist the tension developed in the cell architecture. They are known to grow under the application of an external force, and to shrink when internal tension is decreased (11-13). Thus, many recent studies investigated the correlation between local traction forces and maturation of individual FAs using 2D deformable substrates (14-18).However, to understand how the cell spread area could control cell fate, a description of the link between the overall cell shape and FA dynamics is still missing. Noteworthily, cell traction forces (19,20) and cell signaling (1, 3, 6) were shown to be nonlinear functions of the cell spread area. In other words, the magnitude of traction forces, the fraction of apoptotic cells, or the level of histone acetylation present a switch from a low to...