Cells as liquid motors: mechanosensitivity emerges from collective dynamics of actomyosin cortex

Active viscoelastic models for cell and tissue mechanics

Living cells are out of equilibrium active materials. Cell-generated forces are transmitted across the cytoskeleton network and to the extracellular environment. These active force interactions shape cellular mechanical behaviour, trigger mechano-sensing, regulate cell adaptation to the microenvironment and can affect disease outcomes. In recent years, the mechanobiology community has witnessed the emergence of many experimental and theoretical approaches to study cells as mechanically active materials. In this review, we highlight recent advancements in incorporating active characteristics of cellular behaviour at different length scales into classic viscoelastic models by either adding an active tension-generating element or adjusting the resting length of an elastic element in the model. Summarizing the two groups of approaches, we will review the formulation and application of these models to understand cellular adaptation mechanisms in response to various types of mechanical stimuli, such as the effect of extracellular matrix properties and external loadings or deformations.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Mapping cell cortex rheology to tissue rheology and vice versa

The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behavior. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low-frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behavior has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

Lymph node homeostasis and adaptation to immune challenge resolved by fibroblast network mechanics

Emergent physical properties of tissues are not readily understood by reductionist studies of their constituent cells. Here, we show molecular signals controlling cellular, physical, and structural properties and collectively determine tissue mechanics of lymph nodes, an immunologically relevant adult tissue. Lymph nodes paradoxically maintain robust tissue architecture in homeostasis yet are continually poised for extensive expansion upon immune challenge. We find that in murine models of immune challenge, cytoskeletal mechanics of a cellular meshwork of fibroblasts determine tissue tension independently of extracellular matrix scaffolds. We determine that C-type lectin-like receptor 2 (CLEC-2)-podoplanin signaling regulates the cell surface mechanics of fibroblasts, providing a mechanically sensitive pathway to regulate lymph node remodeling. Perturbation of fibroblast mechanics through genetic deletion of podoplanin attenuates T cell activation. We find that increased tissue tension through the fibroblastic stromal meshwork is required to trigger the initiation of fibroblast proliferation and restore homeostatic cellular ratios and tissue structure through lymph node expansion.

Embryo-scale epithelial buckling forms a propagating furrow that initiates gastrulation

Cell apical constriction driven by actomyosin contraction forces is a conserved mechanism during tissue folding in embryo development. While much is now understood of the molecular mechanism responsible for apical constriction and of the tissue-scale integration of the ensuing in-plane deformations, it is still not clear if apical actomyosin contraction forces are necessary or sufficient per se to drive tissue folding. To tackle this question, we use the Drosophila embryo model system that forms a furrow on the ventral side, initiating mesoderm internalization. Past computational models support the idea that cell apical contraction forces may not be sufficient and that active or passive cell apico-basal forces may be necessary to drive cell wedging leading to tissue furrowing. By using 3D computational modelling and in toto embryo image analysis and manipulation, we now challenge this idea and show that embryo-scale force balance at the tissue surface, rather than cell-autonomous shape changes, is necessary and sufficient to drive a buckling of the epithelial surface forming a furrow which propagates and initiates embryo gastrulation.

Drosophila mesoderm invagination begins with the formation of a furrow. Here they show that a long-range mechanism, powered by actomyosin contraction between the embryo polar caps, works like a ‘cheese-cutter wire’ indenting the tissue surface and folding it into a propagating furrow.

Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model

Cell intercalation is a key cell behaviour of morphogenesis and wound healing, where local cell neighbour exchanges can cause dramatic tissue deformations such as body axis extension. Substantial experimental work has identified the key molecular players facilitating intercalation, but there remains a lack of consensus and understanding of their physical roles. Existing biophysical models that represent cell-cell contacts with single edges cannot study cell neighbour exchange as a continuous process, where neighbouring cell cortices must uncouple. Here, we develop an Apposed-Cortex Adhesion Model (ACAM) to understand active cell intercalation behaviours in the context of a 2D epithelial tissue. The junctional actomyosin cortex of every cell is modelled as a continuous viscoelastic rope-loop, explicitly representing cortices facing each other at bicellular junctions and the adhesion molecules that couple them. The model parameters relate directly to the properties of the key subcellular players that drive dynamics, providing a multi-scale understanding of cell behaviours. We show that active cell neighbour exchanges can be driven by purely junctional mechanisms. Active contractility and cortical turnover in a single bicellular junction are sufficient to shrink and remove a junction. Next, a new, orthogonal junction extends passively. The ACAM reveals how the turnover of adhesion molecules regulates tension transmission and junction deformation rates by controlling slippage between apposed cell cortices. The model additionally predicts that rosettes, which form when a vertex becomes common to many cells, are more likely to occur in actively intercalating tissues with strong friction from adhesion molecules.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.

Rapid viscoelastic changes are a hallmark of early leukocyte activation

To accomplish their critical task of removing infected cells and fighting pathogens, leukocytes activate by forming specialized interfaces with other cells. The physics of this key immunological process are poorly understood, but it is important to understand them because leukocytes have been shown to react to their mechanical environment. Using an innovative micropipette rheometer, we show in three different types of leukocytes that, when stimulated by microbeads mimicking target cells, leukocytes become up to 10 times stiffer and more viscous. These mechanical changes start within seconds after contact and evolve rapidly over minutes. Remarkably, leukocyte elastic and viscous properties evolve in parallel, preserving a well-defined ratio that constitutes a mechanical signature specific to each cell type. Our results indicate that simultaneously tracking both elastic and viscous properties during an active cell process provides a new, to our knowledge, way to investigate cell mechanical processes. Our findings also suggest that dynamic immunomechanical measurements can help discriminate between leukocyte subtypes during activation.

Development of an FEA framework for analysis of subject-specific aortic compliance based on 4D flow MRI

This paper presents a subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel during the cardiac cycle uncovered through our MRI investigations. A microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle cell stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle cell contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin digestion and SMC activation experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower distally. The analyses presented in this paper provide new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. Furthermore, this subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development. STATEMENT OF SIGNIFICANCE: This study provides a significant advance in in-silico medicine by capturing the structure/function relationship of the subject-specific human aorta presented in our previous MRI analyses. A physiologically based aortic constitutive model is developed, and simulations reveal that internal vessel contractility must be incorporated, along with collagen strain stiffening, to accurately predict the in-vivo non-linear pressure-area relationship. Furthermore, this is the first subject-specific model to predict spatial variation in the volume fractions of aortic wall constituents. Previous studies perform phenomenological hyperelastic curve fits to medical imaging data and ignore the prestress contribution of elastin, collagen, and SMCs and the associated zero-pressure reference state of the vessel. This novel MRI/FEA framework can be used as an in-silico diagnostic tool for the early stage detection of aortic pathologies.

Durotaxis: the mechanical control of directed cell migration

Directed cell migration is essential for cells to efficiently migrate in physiological and pathological processes. While migrating in their native environment, cells interact with multiple types of cues, such as mechanical and chemical signals. The role of chemical guidance via chemotaxis has been studied in the past, the understanding of mechanical guidance of cell migration via durotaxis remained unclear until very recently. Nonetheless, durotaxis has become a topic of intensive research and several advances have been made in the study of mechanically guided cell migration across multiple fields. Thus, in this article we provide a state of the art about durotaxis by discussing in silico, in vitro and in vivo data. We also present insights on the general mechanisms by which cells sense, transduce and respond to environmental mechanics, to then contextualize these mechanisms in the process of durotaxis and explain how cells bias their migration in anisotropic substrates. Furthermore, we discuss what is known about durotaxis in vivo and we comment on how haptotaxis could arise from integrating durotaxis and chemotaxis in native environments.

Substrate Resistance to Traction Forces Controls Fibroblast Polarization

The mechanics of fibronectin-rich extracellular matrix regulate cell physiology in a number of diseases, prompting efforts to elucidate cell mechanosensing mechanisms at the molecular and cellular scale. Here, the use of fibronectin-functionalized silicone elastomers that exhibit considerable frequency dependence in viscoelastic properties unveiled the presence of two cellular processes that respond discreetly to substrate mechanical properties. Weakly cross-linked elastomers supported efficient focal adhesion maturation and fibroblast spreading because of an apparent stiff surface layer. However, they did not enable cytoskeletal and fibroblast polarization; elastomers with high cross-linking and low deformability were required for polarization. Our results suggest as an underlying reason for this behavior the inability of soft elastomer substrates to resist traction forces rather than a lack of sufficient traction force generation. Accordingly, mild inhibition of actomyosin contractility rescued fibroblast polarization even on the softer elastomers. Our findings demonstrate differential dependence of substrate physical properties on distinct mechanosensitive processes and provide a premise to reconcile previously proposed local and global models of cell mechanosensing.

Self-organized cytoskeletal alignment during Drosophila mesoderm invagination

During tissue morphogenesis, mechanical forces are propagated across tissues, resulting in tissue shape changes. These forces in turn can influence cell behaviour, leading to a feedback process that can be described as self-organizing. Here, I discuss cytoskeletal self-organization and point to evidence that suggests its role in directing force during morphogenesis. During Drosophila mesoderm invagination, the shape of the region of cells that initiates constriction creates a mechanical pattern that in turn aligns the cytoskeleton with the axis of greatest resistance to contraction. The wild-type direction of the force controls the shape and orientation of the invaginating mesoderm. Given the ability of the actomyosin cytoskeleton to self-organize, these types of feedback mechanisms are likely to play important roles in a range of different morphogenetic events. This article is part of the discussion meeting issue 'Contemporary morphogenesis'.

Migrating Epithelial Monolayer Flows Like a Maxwell Viscoelastic Liquid

We perform a bidimensional Stokes experiment in an active cellular material: an autonomously migrating monolayer of Madin-Darby canine kidney epithelial cells flows around a circular obstacle within a long and narrow channel, involving an interplay between cell shape changes and neighbor rearrangements. Based on image analysis of tissue flow and coarse-grained cell anisotropy, we determine the tissue strain rate, cell deformation, and rearrangement rate fields, which are spatially heterogeneous. We find that the cell deformation and rearrangement rate fields correlate strongly, which is compatible with a Maxwell viscoelastic liquid behavior (and not with a Kelvin-Voigt viscoelastic solid behavior). The value of the associated relaxation time is measured as τ=70±15  min, is observed to be independent of obstacle size and division rate, and is increased by inhibiting myosin activity. In this experiment, the monolayer behaves as a flowing material with a Weissenberg number close to one which shows that both elastic and viscous effects can have comparable contributions in the process of collective cell migration.

Tug-of-war between stretching and bending in living cell sheets

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness e of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like 1/e, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

Mechanical interplay between cell shape and actin cytoskeleton organization

We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses. Upon modeling the actin cytoskeleton as a nematic liquid crystal, we further show that the geometry of the cell edge feeds back on the organization of the stress fibers by altering the length scale at which these are confined. This feedback mechanism is controlled by a dimensionless number, the anchoring number, representing the relative weight of surface-anchoring and bulk-aligning torques. Our model allows to predict both cellular shape and the internal structure of the actin cytoskeleton and is in good quantitative agreement with experiments on fibroblastoid (GDβ1, GDβ3) and epithelioid (GEβ1, GEβ3) cells.

Cell response to substrate rigidity is regulated by active and passive cytoskeletal stress

Morphogenesis, tumor formation, and wound healing are regulated by tissue rigidity. Focal adhesion behavior is locally regulated by stiffness; however, how cells globally adapt, detect, and respond to rigidity remains unknown. Here, we studied the interplay between the rheological properties of the cytoskeleton and matrix rigidity. We seeded fibroblasts onto flexible microfabricated pillar arrays with varying stiffness and simultaneously measured the cytoskeleton organization, traction forces, and cell-rigidity responses at both the adhesion and cell scale. Cells adopted a rigidity-dependent phenotype whereby the actin cytoskeleton polarized on stiff substrates but not on soft. We further showed a crucial role of active and passive cross-linkers in rigidity-sensing responses. By reducing myosin II activity or knocking down α-actinin, we found that both promoted cell polarization on soft substrates, whereas α-actinin overexpression prevented polarization on stiff substrates. Atomic force microscopy indentation experiments showed that this polarization response correlated with cell stiffness, whereby cell stiffness decreased when active or passive cross-linking was reduced and softer cells polarized on softer matrices. Theoretical modeling of the actin network as an active gel suggests that adaptation to matrix rigidity is controlled by internal mechanical properties of the cytoskeleton and puts forward a universal scaling between nematic order of the actin cytoskeleton and the substrate-to-cell elastic modulus ratio. Altogether, our study demonstrates the implication of cell-scale mechanosensing through the internal stress within the actomyosin cytoskeleton and its coupling with local rigidity sensing at focal adhesions in the regulation of cell shape changes and polarity.

Actomyosin controls planarity and folding of epithelia in response to compression

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 that 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.

Stiffness Sensing by Cells

Physical stimuli are essential for the function of eukaryotic cells, and changes in physical signals are important elements in normal tissue development as well as in disease initiation and progression. The complexity of physical stimuli and the cellular signals they initiate are as complex as those triggered by chemical signals. One of the most important, and the focus of this review, is the effect of substrate mechanical properties on cell structure and function. The past decade has produced a nearly exponentially increasing number of mechanobiological studies to define how substrate stiffness alters cell biology using both purified systems and intact tissues. Here we attempt to identify common features of mechanosensing in different systems while also highlighting the numerous informative exceptions to what in early studies appeared to be simple rules by which cells respond to mechanical stresses.

Feeling Stressed or Strained? A Biophysical Model for Cell Wall Mechanosensing in Plants

Mechanical signals have recently emerged as a major cue in plant morphogenesis, notably influencing cytoskeleton organization, gene expression, protein polarity, or cell division. Although many putative mechanosensing proteins have been identified, it is unclear what mechanical cue they might sense and how this would occur. Here we briefly explain the notions of mechanical stress and strain. We present the challenges to understand their sensing by plants, focusing on the cell wall and the plasma membrane, and we review putative mechanosensing structures. We propose minimal biophysical models of mechanosensing, revealing the modes of mechanosensing according to mechanosensor lifetime, threshold force for mechanosensor dissociation, and type of association between the mechanosensor and the cell wall, as the sensor may be associated to a major load-bearing structure such as cellulose or to a minor load-bearing structure such as pectins or the plasma membrane. Permanent strain, permanent expansion, and relatively slow variations thereof are sensed in all cases; variations of stress are sensed in all cases; permanent stress is sensed only in the following specific cases: sensors associated to minor load-bearing structures slowly relaxing in a growing wall, long-lived sensors with high dissociation force and associated to major-load-bearing structures, and sensors with low dissociation force associated to major-load-baring structures behaving elastically. We also find that all sensors respond to variations in the composition or the mechanical properties of the cell wall. The level of sensing is modulated by the properties of all of mechanosensor, cell wall components, and plasma membrane. Although our models are minimal and not fully realistic, our results yield a framework to start investigating the possible functions of putative mechanosensors.

Biotensegrity or Fascintegrity?

The biotensegrity view of the living is a theoretical model and there is no mathematical study in vitro or in vivo that demonstrates its validity, taking into account the presence of liquids (blood, lymph, water), the tension produced by nerves and blood vessels, just as the displacement of the viscera and their resistances and contractions are not taken into consideration. The concept of cellular transduction is reviewed as it is the key to understanding if the passage of different mechanical information occurs only through solid structures, such as the cytoskeleton, or even liquid and viscous. The article focuses on reviewing the weaknesses of the biotensegrity model in the light of new scientific information, trying to coin another term that better reflects the dynamics of living: fascintegrity.

Dynamic fibroblast contractions attract remote macrophages in fibrillar collagen matrix

Macrophage (Mϕ)-fibroblast interactions coordinate tissue repair after injury whereas miscommunications can result in pathological healing and fibrosis. We show that contracting fibroblasts generate deformation fields in fibrillar collagen matrix that provide far-reaching physical cues for Mϕ. Within collagen deformation fields created by fibroblasts or actuated microneedles, Mϕ migrate towards the force source from several hundreds of micrometers away. The presence of a dynamic force source in the matrix is critical to initiate and direct Mϕ migration. In contrast, collagen condensation and fiber alignment resulting from fibroblast remodelling activities or chemotactic signals are neither required nor sufficient to guide Mϕ migration. Binding of α2β1 integrin and stretch-activated channels mediate Mϕ migration and mechanosensing in fibrillar collagen ECM. We propose that Mϕ mechanosense the velocity of local displacements of their substrate, allowing contractile fibroblasts to attract Mϕ over distances that exceed the range of chemotactic gradients.

Macrophages play an important role in wound healing but the guidance cues driving macrophages to sites of repair are still not clear. Here the authors discover that macrophages are attracted to contracting fibroblasts by responding to locally sensed displacements of collagen fibres.

Low-energy shock waves evoke intracellular Ca2+ increases independently of sonoporation

Low-energy shock waves (LESWs) accelerate the healing of a broad range of tissue injuries, including angiogenesis and bone fractures. In cells, LESW irradiations enhance gene expression and protein synthesis. One probable mechanism underlying the enhancements is mechanosensing. Shock waves also can induce sonoporation. Thus, sonoporation is another probable mechanism underlying the enhancements. It remains elusive whether LESWs require sonoporation to evoke cellular responses. An intracellular Ca²⁺ increase was evoked with LESW irradiations in endothelial cells. The minimum acoustic energy required for sufficient evocation was 1.7 μJ/mm². With the same acoustic energy, sonoporation, by which calcein and propidium iodide would become permeated, was not observed. It was found that intracellular Ca²⁺ increases evoked by LESW irradiations do not require sonoporation. In the intracellular Ca²⁺ increase, actin cytoskeletons and stretch-activated Ca²⁺ channels were involved; however, microtubules were not. In addition, with Ca²⁺ influx through the Ca²⁺ channels, the Ca²⁺ release through the PLC-IP₃-IP₃R cascade contributed to the intracellular Ca²⁺ increase. These results demonstrate that LESW irradiations can evoke cellular responses independently of sonoporation. Rather, LESW irradiations evoke cellular responses through mechanosensing.

Mechanosensitivity of Cancer Cells in Contact with Soft Substrates Using AFM

Cancer cells are usually found to be softer than normal cells, but their stiffness changes when they are in contact with different environments because of mechanosensitivity. For example, they adhere to a given substrate by tuning their cytoskeleton, thus affecting their rheological properties. This mechanism could become efficient when cancer cells invade the surrounding tissues, and they have to remodel their cytoskeleton in order to achieve particular deformations. Here we use an atomic force microscope in force modulation mode to study how local rheological properties of cancer cells are affected by a change of the environment. Cancer cells were plated on functionalized polyacrylamide substrates of different stiffnesses as well as on an endothelium substrate. A new correction of the Hertz model was developed because measurements require one to account for the precise properties of the thin, layered viscoelastic substrates. The main results show the influence of local cell rheology (the nucleus, perinuclear region, and edge locations) and the role of invasiveness. A general mechanosensitive trend is found by which the cell elastic modulus and transition frequency increase with substrate elasticity, but this tendency breaks down with a real endothelium substrate. These effects are investigated further during cell transmigration, when the actin cytoskeleton undergoes a rapid reorganization process necessary to push through the endothelial gap, in agreement with the local viscoelastic changes measured by atomic force microscopy. Taken together, these results introduce a paradigm for a new-to our knowledge-possible extravasation mechanism.

The Awareness of the Fascial System

Fascia is a cacophony of functions and information, a completely adaptable entropy complex. The fascial system has a solid and a liquid component, acting in a perfect symbiotic synchrony. Each cell communicates with the other cells by sending and receiving signals; this concept is a part of quantum physics and it is known as quantum entanglement: a physical system cannot be described individually, but only as a juxtaposition of multiple systems, where the measurement of a quantity determines the value for other systems. Fascial continuum serves as a target for different manual approaches, such as physiotherapy, osteopathy and chiropractic. Cellular behaviour and the inclusion of quantum physics background are hardly being considered to find out what happens between the operator and the patient during a manual physical contact. The article examines these topics. According to the authors' knowledge, this is the first scientific text to offer manual operators’ new perspectives to understand what happens during palpatory contact. A fascial cell has not only memory but also the awareness of the mechanometabolic information it feels, and it has the anticipatory predisposition in preparing itself for alteration of its natural environment.

Emergent mechanics of actomyosin drive punctuated contractions and shape network morphology in the cell cortex

Filamentous actin (F-actin) and non-muscle myosin II motors drive cell motility and cell shape changes that guide large scale tissue movements during embryonic morphogenesis. To gain a better understanding of the role of actomyosin in vivo, we have developed a two-dimensional (2D) computational model to study emergent phenomena of dynamic unbranched actomyosin arrays in the cell cortex. These phenomena include actomyosin punctuated contractions, or "actin asters" that form within quiescent F-actin networks. Punctuated contractions involve both formation of high intensity aster-like structures and disassembly of those same structures. Our 2D model allows us to explore the kinematics of filament polarity sorting, segregation of motors, and morphology of F-actin arrays that emerge as the model structure and biophysical properties are varied. Our model demonstrates the complex, emergent feedback between filament reorganization and motor transport that generate as well as disassemble actin asters. Since intracellular actomyosin dynamics are thought to be controlled by localization of scaffold proteins that bind F-actin or their myosin motors we also apply our 2D model to recapitulate in vitro studies that have revealed complex patterns of actomyosin that assemble from patterning filaments and motor complexes with microcontact printing. Although we use a minimal representation of filament, motor, and cross-linker biophysics, our model establishes a framework for investigating the role of other actin binding proteins, how they might alter actomyosin dynamics, and makes predictions that can be tested experimentally within live cells as well as within in vitro models.

Recent genetic and mechanical studies of embryonic development reveal a critical role for intracellular scaffolds in generating the shape of the embryo and constructing internal organs. In this paper we developed computer simulations of these scaffolds, composed of filamentous actin (F-actin), a rod-like protein polymer, and mini-thick filaments, composed of non-muscle myosin II, forming a two headed spring-like complex of motor proteins that can walk on, and remodel F-actin networks. Using simulations of these dynamic interactions, we can carry out virtual experiments where we change the physics and chemistry of F-actin polymers, their associated myosin motors, and cross-linkers and observe the changes in scaffolds that emerge. For example, by modulating the motor stiffness of the myosin motors in our model we can observe the formation or loss of large aster-like structures. Such fine-grained control over the physical properties of motors or filaments within simulations are not currently possible with biological experiments, even where mutant proteins or small molecule inhibitors can be targeted to specific sites on filaments or motors. Our approach reflects a growing adoption of simulation methods to investigate microscopic features that shape actomyosin arrays and the mesoscale effects of molecular scale processes. We expect predictions from these models will drive more refined experimental approaches to expose the many roles of actomyosin in development.

Matching material and cellular timescales maximizes cell spreading on viscoelastic substrates

Recent evidence has shown that, in addition to rigidity, the viscous response of the extracellular matrix (ECM) significantly affects the behavior and function of cells. However, the mechanism behind such mechanosensitivity toward viscoelasticity remains unclear. In this study, we systematically examined the dynamics of motor clutches (i.e., focal adhesions) formed between the cell and a viscoelastic substrate using analytical methods and direct Monte Carlo simulation. Interestingly, we observe that, for low ECM rigidity, maximum cell spreading is achieved at an optimal level of viscosity in which the substrate relaxation time falls between the timescale for clutch binding and its characteristic binding lifetime. That is, viscosity serves to stiffen soft substrates on a timescale faster than the clutch off-rate, which enhances cell-ECM adhesion and cell spreading. On the other hand, for substrates that are stiff, our model predicts that viscosity will not influence cell spreading, since the bound clutches are saturated by the elevated stiffness. The model was tested and validated using experimental measurements on three different material systems and explained the different observed effects of viscosity on each substrate. By capturing the mechanism by which substrate viscoelasticity affects cell spreading across a wide range of material parameters, our analytical model provides a useful tool for designing biomaterials that optimize cellular adhesion and mechanosensing.

Taking the strain: quantifying the contributions of all cell behaviours to changes in epithelial shape

Computer-assisted tracking of the shapes of many cells over long periods of development has driven the exploration of novel ways to quantify the contributions of different cell behaviours to morphogenesis. A handful of similar methods have now been published that are used to calculate tissue deformations (strain rates) in epithelia. These methods are further used to quantify strain rates attributable to each of the cell behaviours in the tissue, such as cell shape change, cell rearrangement and cell division, that together sum to the tissue strain rates. In this review, aimed at developmental biologists, I will introduce the general approach, characterize differences in current approaches and highlight extensions of these methods that remain to be fully explored. The methods will make a major contribution to the emerging field of tissue mechanics. Precisely quantified strain rates are an essential first step towards exploring constitutive equations relating stress to strain via tissue mechanical properties.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

The Nuclear Option: Evidence Implicating the Cell Nucleus in Mechanotransduction

Biophysical stimuli presented to cells via microenvironmental properties (e.g., alignment and stiffness) or external forces have a significant impact on cell function and behavior. Recently, the cell nucleus has been identified as a mechanosensitive organelle that contributes to the perception and response to mechanical stimuli. However, the specific mechanotransduction mechanisms that mediate these effects have not been clearly established. Here, we offer a comprehensive review of the evidence supporting (and refuting) three hypothetical nuclear mechanotransduction mechanisms: physical reorganization of chromatin, signaling at the nuclear envelope, and altered cytoskeletal structure/tension due to nuclear remodeling. Our goal is to provide a reference detailing the progress that has been made and the areas that still require investigation regarding the role of nuclear mechanotransduction in cell biology. Additionally, we will briefly discuss the role that mathematical models of cell mechanics can play in testing these hypotheses and in elucidating how biophysical stimulation of the nucleus drives changes in cell behavior. While force-induced alterations in signaling pathways involving lamina-associated polypeptides (LAPs) (e.g., emerin and histone deacetylase 3 (HDAC3)) and transcription factors (TFs) located at the nuclear envelope currently appear to be the most clearly supported mechanism of nuclear mechanotransduction, additional work is required to examine this process in detail and to more fully test alternative mechanisms. The combination of sophisticated experimental techniques and advanced mathematical models is necessary to enhance our understanding of the role of the nucleus in the mechanotransduction processes driving numerous critical cell functions.

Adaptation trajectories during adhesion and spreading affect future cell states

Cells are complex systems in which dynamic gene expression and protein-interaction networks adapt to changes in the environment. Seeding and subsequent spreading of cells on substrates represents an example of adaptation to a major perturbation. The formation of adhesive interactions and self-organisation of the cytoskeleton during initial spreading might prime future cell behaviour. To elucidate the role of these events on later cellular behaviour, we mapped the trajectories by which cells respond to seeding on substrates with different physical properties. Our experiments on cell spreading dynamics on collagen- or fibrin-coated polyacrylamide gels and collagen or fibrin hydrogels show that on each substrate, cells follow distinct trajectories of morphological changes, culminating in fundamentally different cell states as quantified by RNA-expression levels, YAP/TAZ localisation, proliferation and differentiation propensities. The continuous adaptation of the cell to environmental cues leaves traces due to differential cellular organisation and gene expression profiles, blurring correlations between a particular physical property and cellular phenotype.

Micropipette force probe to quantify single-cell force generation: application to T-cell activation

We describe the micropipette force probe, a novel technique that uses a micropipette as a flexible cantilever that aspirates a coated microbead and brings it into contact with a cell. We apply the technique to quantify mechanical and morphological events occurring during T-cell activation.

In response to engagement of surface molecules, cells generate active forces that regulate many cellular processes. Developing tools that permit gathering mechanical and morphological information on these forces is of the utmost importance. Here we describe a new technique, the micropipette force probe, that uses a micropipette as a flexible cantilever that can aspirate at its tip a bead that is coated with molecules of interest and is brought in contact with the cell. This technique simultaneously allows tracking the resulting changes in cell morphology and mechanics as well as measuring the forces generated by the cell. To illustrate the power of this technique, we applied it to the study of human primary T lymphocytes (T-cells). It allowed the fine monitoring of pushing and pulling forces generated by T-cells in response to various activating antibodies and bending stiffness of the micropipette. We further dissected the sequence of mechanical and morphological events occurring during T-cell activation to model force generation and to reveal heterogeneity in the cell population studied. We also report the first measurement of the changes in Young’s modulus of T-cells during their activation, showing that T-cells stiffen within the first minutes of the activation process.

Actomyosin meshwork mechanosensing enables tissue shape to orient cell force

Sculpting organism shape requires that cells produce forces with proper directionality. Thus, it is critical to understand how cells orient the cytoskeleton to produce forces that deform tissues. During Drosophila gastrulation, actomyosin contraction in ventral cells generates a long, narrow epithelial furrow, termed the ventral furrow, in which actomyosin fibres and tension are directed along the length of the furrow. Using a combination of genetic and mechanical perturbations that alter tissue shape, we demonstrate that geometrical and mechanical constraints act as cues to orient the cytoskeleton and tension during ventral furrow formation. We developed an in silico model of two-dimensional actomyosin meshwork contraction, demonstrating that actomyosin meshworks exhibit an inherent force orienting mechanism in response to mechanical constraints. Together, our in vivo and in silico data provide a framework for understanding how cells orient force generation, establishing a role for geometrical and mechanical patterning of force production in tissues.

Large-scale tissue reorganization requires the generation of directional tension, which requires orientation of the cytoskeleton. Here Chanet et al. alter tissue shape and tension in the Drosophila embryo to show that geometric and mechanical constraints act as cues to orient the cytoskeleton and tension.

Geometry can provide long-range mechanical guidance for embryogenesis

Downstream of gene expression, effectors such as the actomyosin contractile machinery drive embryo morphogenesis. During Drosophila embryonic axis extension, actomyosin has a specific planar-polarised organisation, which is responsible for oriented cell intercalation. In addition to these cell rearrangements, cell shape changes also contribute to tissue deformation. While cell-autonomous dynamics are well described, understanding the tissue-scale behaviour challenges us to solve the corresponding mechanical problem at the scale of the whole embryo, since mechanical resistance of all neighbouring epithelia will feedback on individual cells. Here we propose a novel numerical approach to compute the whole-embryo dynamics of the actomyosin-rich apical epithelial surface. We input in the model specific patterns of actomyosin contractility, such as the planar-polarisation of actomyosin in defined ventro-lateral regions of the embryo. Tissue strain rates and displacements are then predicted over the whole embryo surface according to the global balance of stresses and the material behaviour of the epithelium. Epithelia are modelled using a rheological law that relates the rate of deformation to the local stresses and actomyosin anisotropic contractility. Predicted flow patterns are consistent with the cell flows observed when imaging Drosophila axis extension in toto, using light sheet microscopy. The agreement between model and experimental data indicates that the anisotropic contractility of planar-polarised actomyosin in the ventro-lateral germband tissue can directly cause the tissue-scale deformations of the whole embryo. The three-dimensional mechanical balance is dependent on the geometry of the embryo, whose curved surface is taken into account in the simulations. Importantly, we find that to reproduce experimental flows, the model requires the presence of the cephalic furrow, a fold located anteriorly of the extending tissues. The presence of this geometric feature, through the global mechanical balance, guides the flow and orients extension towards the posterior end.

Regulatory Roles of Fluctuation-Driven Mechanotransduction in Cell Function

Cells in the body are exposed to irregular mechanical stimuli. Here, we review the so-called fluctuation-driven mechanotransduction in which stresses stretching cells vary on a cycle-by-cycle basis. We argue that such mechanotransduction is an emergent network phenomenon and offer several potential mechanisms of how it regulates cell function. Several examples from the vasculature, the lung, and tissue engineering are discussed. We conclude with a list of important open questions.

Prediction of traction forces of motile cells

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.

Rigidity generation by nonthermal fluctuations

Active stabilization in systems with zero or negative stiffness is an essential element of a wide variety of biological processes. We study a prototypical example of this phenomenon and show how active rigidity, interpreted as a formation of a pseudowell in the effective energy landscape, can be generated in an overdamped stochastic system. We link the transition from negative to positive rigidity with time correlations in the additive noise, and we show that subtle differences in the out-of-equilibrium driving may compromise the emergence of a pseudowell.

Mechanical regulation of a molecular clutch defines force transmission and transduction in response to matrix rigidity

Cell function depends on tissue rigidity, which cells probe by applying and transmitting forces to their extracellular matrix, and then transducing them into biochemical signals. Here we show that in response to matrix rigidity and density, force transmission and transduction are explained by the mechanical properties of the actin-talin-integrin-fibronectin clutch. We demonstrate that force transmission is regulated by a dynamic clutch mechanism, which unveils its fundamental biphasic force/rigidity relationship on talin depletion. Force transduction is triggered by talin unfolding above a stiffness threshold. Below this threshold, integrins unbind and release force before talin can unfold. Above the threshold, talin unfolds and binds to vinculin, leading to adhesion growth and YAP nuclear translocation. Matrix density, myosin contractility, integrin ligation and talin mechanical stability differently and nonlinearly regulate both force transmission and the transduction threshold. In all cases, coupling of talin unfolding dynamics to a theoretical clutch model quantitatively predicts cell response.

Phase diagram of a tubular vesicle adhering between two parallel rigid planes

In this study, we propose a two-dimensional (2D) theoretical model to explore the adhesion behavior of a tubular vesicle adhering between two rigid planes, which are constrained by a couple of forces. Based upon the free-energy functional of the system, the equations for the equilibrium shape are derived. The general solution for the system with zero pressure is obtained analytically and the stability of the corresponding equilibrium shapes is tested by numerical simulation. With the volume constraint, three kinds of typical stable shapes are obtained through scanning the parameter space numerically. The phase diagram is obtained and it is occupied mostly by nonsymmetrical shapes. The force-displacement curves obtained for our model are in agreement with experimental results. The catastrophe of force is found at a critical state, which reveals a huge expanding force will act on the two planes by the vesicle. It also implies that vesicles can spontaneously squeeze into a slit only due to adhesion.

A question of time: tissue adaptation to mechanical forces

While much attention has been focused on the force-generating mechanisms responsible for shaping developing embryos, less is known about the ways in which cells in animal tissues respond to mechanical stimuli. Forces will arise within a tissue as the result of processes such as local cell death, growth and division, but they can also be an indirect consequence of morphogenetic movements in neighbouring tissues or be imposed from the outside, for example, by gravity. If not dealt with, the accumulation of stress and the resulting tissue deformation can pose a threat to tissue integrity and structure. Here we follow the time-course of events by which cells and tissues return to their preferred state following a mechanical perturbation. In doing so, we discuss the spectrum of biological and physical mechanisms known to underlie mechanical homeostasis in animal tissues.

Contribution of myosin II activity to cell spreading dynamics

Myosin II activity and actin polymerization at the leading edge of the cell are known to be essential sources of cellular stress. However, a quantitative account of their separate contributions is still lacking; so is the influence of the coupling between the two phenomena on cell spreading dynamics. We present a simple analytic elastic theory of cell spreading dynamics that quantitatively demonstrates how actin polymerization and myosin activity cooperate in the generation of cellular stress during spreading. Consistent with experiments, myosin activity is assumed to polarize in response to the stresses generated during spreading. The characteristic response time and the overall spreading time are predicted to determine different evolution profiles of cell spreading dynamics. These include, a (regular) monotonic increase of cell projected area with time, a non-monotonic (overshooting) profile with a maximum, and damped oscillatory modes. In addition, two populations of myosin II motors are distinguished based on their location in the lamella; those located above the major adhesion zone at the cell periphery are shown to facilitate spreading whereas those in deeper regions of the lamella are shown to oppose spreading. We demonstrate that the attenuation of myosin activity in the two regions may result in reciprocal effects on spreading. These findings provide important new insight into the function of myosin II motors in the course of spreading.

The Use of Polyacrylamide Hydrogels to Study the Effects of Matrix Stiffness on Nuclear Envelope Properties

Matrix-derived mechanical cues influence cell proliferation, motility, and differentiation. Recent findings clearly demonstrate that the nuclear envelope (NE) adapts and remodels in response to mechanical signals, including matrix stiffness, yet a plethora of studies have been performed on tissue culture plastic or glass that have a similar stiffness to cortical bone. Using methods that allow modulation of matrix stiffness will provide further insight into the role of the NE in physiological conditions and the impact of changes in stiffness observed during ageing and disease on cellular function. In this chapter, we describe the polyacrylamide hydrogel system, which allows fabrication of hydrogels with variable stiffness to better mimic the environment experienced by cells in most tissues of the body.

Emergent material properties of developing epithelial tissues

BACKGROUND

Force generation and the material properties of cells and tissues are central to morphogenesis but remain difficult to measure in vivo. Insight is often limited to the ratios of mechanical properties obtained through disruptive manipulation, and the appropriate models relating stress and strain are unknown. The Drosophila amnioserosa epithelium progressively contracts over 3 hours of dorsal closure, during which cell apices exhibit area fluctuations driven by medial myosin pulses with periods of 1.5-6 min. Linking these two timescales and understanding how pulsatile contractions drive morphogenetic movements is an urgent challenge.

RESULTS

We present a novel framework to measure in a continuous manner the mechanical properties of epithelial cells in the natural context of a tissue undergoing morphogenesis. We show that the relationship between apicomedial myosin fluorescence intensity and strain during fluctuations is consistent with a linear behaviour, although with a lag. We thus used myosin fluorescence intensity as a proxy for active force generation and treated cells as natural experiments of mechanical response under cyclic loading, revealing unambiguous mechanical properties from the hysteresis loop relating stress to strain. Amnioserosa cells can be described as a contractile viscoelastic fluid. We show that their emergent mechanical behaviour can be described by a linear viscoelastic rheology at timescales relevant for tissue morphogenesis. For the first time, we establish relative changes in separate effective mechanical properties in vivo. Over the course of dorsal closure, the tissue solidifies and effective stiffness doubles as net contraction of the tissue commences. Combining our findings with those from previous laser ablation experiments, we show that both apicomedial and junctional stress also increase over time, with the relative increase in apicomedial stress approximately twice that of other obtained measures.

CONCLUSIONS

Our results show that in an epithelial tissue undergoing net contraction, stiffness and stress are coupled. Dorsal closure cell apical contraction is driven by the medial region where the relative increase in stress is greater than that of stiffness. At junctions, by contrast, the relative increase in the mechanical properties is the same, so the junctional contribution to tissue deformation is constant over time. An increase in myosin activity is likely to underlie, at least in part, the change in medioapical properties and we suggest that its greater effect on stress relative to stiffness is fundamental to actomyosin systems and confers on tissues the ability to regulate contraction rates in response to changes in external mechanics.

Multiscale mechanobiology: computational models for integrating molecules to multicellular systems

Mechanical signals exist throughout the biological landscape. Across all scales, these signals, in the form of force, stiffness, and deformations, are generated and processed, resulting in an active mechanobiological circuit that controls many fundamental aspects of life, from protein unfolding and cytoskeletal remodeling to collective cell motions. The multiple scales and complex feedback involved present a challenge for fully understanding the nature of this circuit, particularly in development and disease in which it has been implicated. Computational models that accurately predict and are based on experimental data enable a means to integrate basic principles and explore fine details of mechanosensing and mechanotransduction in and across all levels of biological systems. Here we review recent advances in these models along with supporting and emerging experimental findings.

Active cell mechanics: Measurement and theory

Living cells are active mechanical systems that are able to generate forces. Their structure and shape are primarily determined by biopolymer filaments and molecular motors that form the cytoskeleton. Active force generation requires constant consumption of energy to maintain the nonequilibrium activity to drive organization and transport processes necessary for their function. To understand this activity it is necessary to develop new approaches to probe the underlying physical processes. Active cell mechanics incorporates active molecular-scale force generation into the traditional framework of mechanics of materials. This review highlights recent experimental and theoretical developments towards understanding active cell mechanics. We focus primarily on intracellular mechanical measurements and theoretical advances utilizing the Langevin framework. These developing approaches allow a quantitative understanding of nonequilibrium mechanical activity in living cells. This article is part of a Special Issue entitled: Mechanobiology.

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and ultimately lead to predictions. The newly accessible local information thus calls for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell") and tissue scale ("inter-cell") contributions. We recall the mathematical framework developed for continuum materials and explain how to transform a constitutive equation into a set of partial differential equations amenable to numerical resolution. We show that when plastic behaviour is relevant, the dissipation function formalism appears appropriate to generate constitutive equations; its variational nature facilitates numerical implementation, and we discuss adaptations needed in the case of large deformations. The present article gathers theoretical methods that can readily enhance the significance of the data to be extracted from recent or future high throughput biomechanical experiments.