Acto-myosin based response to stiffness and rigidity sensing

Cells sense the rigidity of their environment and respond to it. Most studies have been focused on the role of adhesion complexes in rigidity sensing. In particular, it has been clearly shown that proteins of the adhesion complexes were stretch-sensitive, and could thus trigger mechano-chemical signaling in response to applied forces. In order to understand how this local mechano-sensitivity could be coordinated at the cell scale, we have recently carried out single cell traction force measurements on springs of varying stiffness. We found that contractility at the cell scale (force, speed of contraction, mechanical power) was indeed adapted to external stiffness, and reflected ATPase activity of non-muscle myosin II and acto-myosin response to load. Here we suggest a scenario of rigidity sensing where local adhesions sensitivity to force could be coordinated by adaptation of the acto-myosin dependent cortical tension at the global cell scale. Such a scenario could explain how spreading and migration are oriented by the rigidity of the cell environment.     

Single cell rigidity sensing: A complex relationship between focal adhesion dynamics and large-scale actin cytoskeleton remodeling

ABSTRACT

Many physiological and pathological processes involve tissue cells sensing the rigidity of their environment. In general, tissue cells have been shown to react to the stiffness of their environment by regulating their level of contractility, and in turn applying traction forces on their environment to probe it. This mechanosensitive process can direct early cell adhesion, cell migration and even cell differentiation. These processes require the integration of signals over time and multiple length scales. Multiple strategies have been developed to understand force- and rigidity-sensing mechanisms and much effort has been concentrated on the study of cell adhesion complexes, such as focal adhesions, and cell cytoskeletons. Here, we review the major biophysical methods used for measuring cell-traction forces as well as the mechanosensitive processes that drive cellular responses to matrix rigidity on 2-dimensional substrates.     

A time-dependent phenomenological model for cell mechano-sensing

Adherent cells normally apply forces as a generic means of sensing and responding to the mechanical nature of their surrounding environment. How these forces vary as a function of the extracellular rigidity is critical to understanding the regulatory functions that drive important phenomena such as wound healing or muscle contraction. In recognition of this fact, experiments have been conducted to understand cell rigidity-sensing properties under known conditions of the extracellular environment, opening new possibilities for modeling this active behavior. In this work, we provide a physics-based constitutive model taking into account the main structural components of the cell to reproduce its most significant contractile properties such as the traction forces exerted as a function of time and the extracellular stiffness. This model shows how the interplay between the time-dependent response of the acto-myosin contractile system and the elastic response of the cell components determines the mechano-sensing behavior of single cells.     

Spatiotemporal analysis of cell response to a rigidity gradient: a quantitative study using multiple optical tweezers

We investigate the dynamic response of single cells to weak and local rigidities, applied at controlled adhesion sites. Using multiple latex beads functionalized with fibronectin, and each trapped in its own optical trap, we study the reaction in real time of single 3T3 fibroblast cells to asymmetrical tensions in the tens of pN · μm⁻¹ range. We show that the cell feels a rigidity gradient even at this low range of tension, and over time develops an adapted change in the force exerted on each adhesion site. The rate at which force increases is proportional to trap stiffness. Actomyosin recruitment is regulated in space and time along the rigidity gradient, resulting in a linear relationship between the amount of recruited actin and the force developed independently in trap stiffness. This time-regulated actomyosin behavior sustains a constant and rigidity-independent velocity of beads inside the traps. Our results show that the strengthening of extracellular matrix-cytoskeleton linkages along a rigidity gradient is regulated by controlling adhesion area and actomyosin recruitment, to maintain a constant deformation of the extracellular matrix.     

Epithelial cell cluster size affects force distribution in response to EGF-induced collective contractility

Several factors present in the extracellular environment regulate epithelial cell adhesion and dynamics. Among them, growth factors such as EGF, upon binding to their receptors at the cell surface, get internalized and directly activate the acto-myosin machinery. In this study we present the effects of EGF on the contractility of epithelial cancer cell colonies in confined geometry of different sizes. We show that the extent to which EGF triggers contractility scales with the cluster size and thus the number of cells. Moreover, the collective contractility results in a radial distribution of traction forces, which are dependent on integrin β1 peripheral adhesions and transmitted to neighboring cells through adherens junctions. Taken together, EGF-induced contractility acts on the mechanical crosstalk and linkage between the cell-cell and cell-matrix compartments, regulating collective responses.     

Dynamic Mechanisms of Cell Rigidity Sensing: Insights from a Computational Model of Actomyosin Networks

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells.     

The consequence of substrates of large-scale rigidity on actin network tension in adherent cells

Abstract

There is compelling evidence that substrate stiffness affects cell adhesion as well as cytoskeleton organization and contractile activity. This work was designed to study the cytoskeletal contractile activity of single cells plated on micropost substrates of different stiffness using a numerical model simulating the intracellular tension of individual cells. We allowed cells to adhere onto micropost substrates of various rigidities and used experimental traction force data to infer cell contractility using a numerical model. The model shows that higher substrate stiffness leads to an increase in intracellular tension. The strength of this model is its ability to calculate the mechanical state of each cell in accordance to its individual cytoskeletal structure. This is achieved by regenerating a numerical cytoskeleton based on microscope images of the actin network of each cell. The resulting numerical structure consequently represents pulling characteristics on its environment similar to those generated by the cell in-vivo. From actin imaging we can calculate and better understand how forces are transmitted throughout the cell.     

The myosin-II-responsive focal adhesion proteome: a tour de force?

The formation and maturation of focal adhesions involves significant changes in protein composition and requires acto-myosin contractility. A mass spectrometry approach reveals changes to the focal adhesion proteome on myosin inhibition, providing a valuable resource for the cell adhesion field.     

The key feature for early migratory processes: Dependence of adhesion,actin bundles,force generation and transmission on filopodia

Migration of cells is one of the most essential prerequisites to form higher organisms and depends on a strongly coordinated sequence of processes. Early migratory events include substrate sensing, adhesion formation, actin bundle assembly and force generation. While substrate sensing was ascribed to filopodia, all other processes were believed to depend mainly on lamellipodia of migrating cells. In this work we show for motile keratinocytes that all processes from substrate sensing to force generation strongly depend on filopodial focal complexes as well as on filopodial actin bundles. In a coordinated step by step process, filopodial focal complexes have to be tightly adhered to the substrate and to filopodial actin bundles to enlarge upon lamellipodial contact forming classical focal adhesions. Lamellipodial actin filaments attached to those focal adhesions originate from filopodia. Upon cell progression, the incorporation of filopodial actin bundles into the lamellipodium goes along with a complete change in actin cross-linker composition from filopodial fascin to lamellipodial α-actinin. α-Actinin in turn is replaced by myosin II and becomes incorporated directly behind the leading edge. Myosin II activity makes this class of actin bundles with their attached FAs the major source of force generation and transmission at the cell front. Furthermore, connection of FAs to force generating actin bundles leads to their stabilization and further enlargement. Consequently, adhesion sites formed independently of filopodia are not connected to detectable actin bundles, transmit weak forces to the substrate and disassemble within a few minutes without having been increased in size.Key words: filopodia, focal complexes, cell migration, focal adhesion, myosin II, force, actin flow, maturation     

From molecular signal activation to locomotion: an integrated, multiscale analysis of cell motility on defined matrices

The adhesion, mechanics, and motility of eukaryotic cells are highly sensitive to the ligand density and stiffness of the extracellular matrix (ECM). This relationship bears profound implications for stem cell engineering, tumor invasion and metastasis. Yet, our quantitative understanding of how ECM biophysical properties, mechanotransductive signals, and assembly of contractile and adhesive structures collude to control these cell behaviors remains extremely limited. Here we present a novel multiscale model of cell migration on ECMs of defined biophysical properties that integrates local activation of biochemical signals with adhesion and force generation at the cell-ECM interface. We capture the mechanosensitivity of individual cellular components by dynamically coupling ECM properties to the activation of Rho and Rac GTPases in specific portions of the cell with actomyosin contractility, cell-ECM adhesion bond formation and rupture, and process extension and retraction. We show that our framework is capable of recreating key experimentally-observed features of the relationship between cell migration and ECM biophysical properties. In particular, our model predicts for the first time recently reported transitions from filopodial to "stick-slip" to gliding motility on ECMs of increasing stiffness, previously observed dependences of migration speed on ECM stiffness and ligand density, and high-resolution measurements of mechanosensitive protrusion dynamics during cell motility we newly obtained for this study. It also relates the biphasic dependence of cell migration speed on ECM stiffness to the tendency of the cell to polarize. By enabling the investigation of experimentally-inaccessible microscale relationships between mechanotransductive signaling, adhesion, and motility, our model offers new insight into how these factors interact with one another to produce complex migration patterns across a variety of ECM conditions.     

Force via integrins but not E-cadherin decreases Oct3/4 expression in embryonic stem cells

Increasing evidence suggests that mechanical factors play a critical role in fate decisions of stem cells. Recently we have demonstrated that a local force applied via Arg-Gly-Asp (RGD) peptides coated magnetic beads to mouse embryonic stem (ES) cells increases cell spreading and cell stiffness and decreases Oct3/4 (Pou5f1) gene expression. However, it is not clear whether the effects of the applied stress on these functions of ES cells can be extended to natural extracellular matrix proteins or cell–cell adhesion molecules. Here we show that a local cyclic shear force applied via fibronectin or laminin to integrin receptors increased cell spreading and stiffness, downregulated Oct3/4 gene expression, and decreased cell proliferation rate. In contrast, the same cyclic force applied via cell–cell adhesion molecule E-cadherin (Cdh1) had no effects on cell spreading, Oct3/4 gene expression, and the self-renewal of mouse ES cells, but induced significant cell stiffening. Our findings demonstrate that biological responses of ES cells to force applied via integrins are different from those to force via E-cadherin, suggesting that mechanical forces might play different roles in different force transduction pathways to shape early embryogenesis.     

A minimal mechanics model for mechanosensing of substrate rigidity gradient in durotaxis

Durotaxis refers to the phenomenon in which cells can sense the spatial gradient of the substrate rigidity in the process of cell migration. A conceptual two-part theory consisting of the focal adhesion force generation and mechanotransduction has been proposed previously by Lo et al. to explain the mechanism underlying durotaxis. In the present work, we are concerned with the first part of the theory: how exactly is the larger focal adhesion force generated in the part of the cell adhering to the stiffer region of the substrate? Using a simple elasticity model and by assuming the cell adheres to the substrate continuously underneath the whole cell body, we show that the mechanics principle of static equilibrium alone is sufficient to account for the generation of the larger traction stress on the stiffer region of the substrate. We believe that our model presents a simple mechanistic understanding of mechanosensing of substrate stiffness gradient at the cellular scale, which can be incorporated in more sophisticated mechanobiochemical models to address complex problems in mechanobiology and bioengineering.     

Prestress and Adhesion Site Dynamics Control Cell Sensitivity to Extracellular Stiffness

This study aims at improving the understanding of mechanisms responsible for cell sensitivity to extracellular environment. We explain how substrate mechanical properties can modulate the force regulation of cell sensitive elements primarily adhesion sites. We present a theoretical and experimental comparison between two radically different approaches of the force regulation of adhesion sites that depends on their either stationary or dynamic behavior. The most classical stationary model fails to predict cell sensitivity to substrate stiffness whereas the dynamic model predicts extracellular stiffness dependence. This is due to a time dependent reaction force in response to actomyosin traction force exerted on cell sensitive elements. We purposely used two cellular models, i.e., alveolar epithelial cells and alveolar macrophages exhibiting respectively stationary and dynamic adhesion sites, and compared their sensitivity to theoretical predictions. Mechanical and structural results show that alveolar epithelial cells exhibit significant prestress supported by evident stress fibers and lacks sensitivity to substrate stiffness. On the other hand, alveolar macrophages exhibit low prestress and exhibit sensitivity to substrate stiffness. Altogether, theory and experiments consistently show that adhesion site dynamics and cytoskeleton prestress control cell sensitivity to extracellular environment with an optimal sensitivity expected in the intermediate range.     

The key feature for early migratory processes

Migration of cells is one of the most essential prerequisites to form higher organisms and depends on a strongly coordinated sequence of processes. Early migratory events include substrate sensing, adhesion formation, actin bundle assembly and force generation. While substrate sensing was ascribed to filopodia, all other processes were believed to depend mainly on lamellipodia of migrating cells. In this work we show for motile keratinocytes that all processes from substrate sensing to force generation strongly depend on filopodial focal complexes as well as on filopodial actin bundles. In a coordinated step by step process filopodial focal complexes have to be tightly adhered to the substrate and to filopodial actin bundles to enlarge upon lamellipodial contact forming classical focal adhesions. Lamellipodial actin filaments attached to those focal adhesions originate from filopodia. Upon cell progression, the incorporation of filopodial actin bundles into the lamellipodium goes along with a complete change in actin cross-linker composition from filopodial fascin to lamellipodial α-actinin. α-Actinin in turn is replaced by myosin II and becomes incorporated directly behind the leading edge. Myosin II activity makes this class of actin bundles with their attached FAs the major source of force generation and transmission at the cell front. Furthermore, connection of FAs to force generating actin bundles leads to their stabilization and further enlargement. Consequently, adhesion sites formed independently of filopodia are not connected to detectable actin bundles, transmit weak forces to the substrate and disassemble within a few minutes without having been increased in size.     

Biochemical and mechanical extracellular matrix properties dictate mammary epithelial cell motility and assembly

Biochemical and mechanical cues of the extracellular matrix have been shown to play important roles in cell-matrix and cell-cell interactions. We have experimentally tested the combined influence of these cues to better understand cell motility, force generation, cell-cell interaction, and assembly in an in vitro breast cancer model. MCF-10A non-tumorigenic mammary epithelial cells were observed on surfaces with varying fibronectin ligand concentration and polyacrylamide gel rigidity. Our data show that cell velocity is biphasic in both matrix rigidity and adhesiveness. The maximum cell migration velocity occurs only at specific combination of substrate stiffness and ligand density. We found cell-cell interactions reduce migration velocity. However, the traction forces cells exert onto the substrate increase linearly with both cues, with cells in pairs exerting higher maximum tractions observed over single cells. A relationship between force and motility shows a maximum in single cell velocity not observed in cell pairs. Cell-cell adhesion becomes strongly favored on softer gels with elasticity ≤ 1250 Pascals (Pa), implying the existence of a compliance threshold that promotes cell-cell over cell-matrix adhesion. Finally on gels with stiffness similar to pre-malignant breast tissue, 400 Pa, cells undergo multicellular assembly and division into 3D spherical aggregates on a 2D surface.     

Cell adhesion strengthening: contributions of adhesive area, integrin binding, and focal adhesion assembly

Mechanical interactions between a cell and its environment regulate migration, contractility, gene expression, and cell fate. We integrated micropatterned substrates to engineer adhesive area and a hydrodynamic assay to analyze fibroblast adhesion strengthening on fibronectin. Independently of cell spreading, integrin binding and focal adhesion assembly resulted in rapid sevenfold increases in adhesion strength to steady-state levels. Adhesive area strongly modulated adhesion strength, integrin binding, and vinculin and talin recruitment, exhibiting linear increases for small areas. However, above a threshold area, adhesion strength and focal adhesion assembly reached a saturation limit, whereas integrin binding transitioned from a uniform distribution to discrete complexes. Adhesion strength exhibited exponential increases with bound integrin numbers as well as vinculin and talin recruitment, and the relationship between adhesion strength and these biochemical events was accurately described by a simple mechanical model. Furthermore, adhesion strength was regulated by the position of an adhesive patch, comprised of bound integrins and cytoskeletal elements, which generated a constant 200-nN adhesive force. Unexpectedly, focal adhesion assembly, in particular vinculin recruitment, contributed only 30% of the adhesion strength. This work elucidates the roles of adhesive complex size and position in the generation of cell-extracellular matrix forces.     

A mathematical model of the coupled mechanisms of cell adhesion,contraction and spreading

Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, the paper describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell’s cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers able to polymerize into an actin meshwork at the cell’s boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. After deriving the governing equation driving the dynamics of cell evolution and spreading, we introduce a numerical solution based on the extended finite element method, combined with a level set formulation. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.     

Cellular contractility and substrate elasticity: a numerical investigation of the actin cytoskeleton and cell adhesion

Numerous experimental studies have established that cells can sense the stiffness of underlying substrates and have quantified the effect of substrate stiffness on stress fibre formation, focal adhesion area, cell traction, and cell shape. In order to capture such behaviour, the current study couples a mixed mode thermodynamic and mechanical framework that predicts focal adhesion formation and growth with a material model that predicts stress fibre formation, contractility, and dissociation in a fully 3D implementation. Simulations reveal that SF contractility plays a critical role in the substrate-dependent response of cells. Compliant substrates do not provide sufficient tension for stress fibre persistence, causing dissociation of stress fibres and lower focal adhesion formation. In contrast, cells on stiffer substrates are predicted to contain large amounts of dominant stress fibres. Different levels of cellular contractility representative of different cell phenotypes are found to alter the range of substrate stiffness that cause the most significant changes in stress fibre and focal adhesion formation. Furthermore, stress fibre and focal adhesion formation evolve as a cell spreads on a substrate and leading to the formation of bands of fibres leading from the cell periphery over the nucleus. Inhibiting the formation of FAs during cell spreading is found to limit stress fibre formation. The predictions of this mutually dependent material-interface framework are strongly supported by experimental observations of cells adhered to elastic substrates and offer insight into the inter-dependent biomechanical processes regulating stress fibre and focal adhesion formation.     

Controlling Cellular Volume via Mechanical and Physical Properties of Substrate

The mechanical and physical properties of substrate play a crucial role in regulating many cell functions and behaviors. However, how these properties affect cell volume is still unclear. Here, we show that an increase in substrate stiffness, available spread area, or effective adhesion energy density results in a remarkable cell volume decrease (up to 50%), and the dynamic cell spreading process is also accompanied by dramatic cell volume decrease. Further, studies of ion channel inhibition and osmotic shock suggest that these volume decreases are due to the efflux of water and ions. We also show that disrupting cortex contractility leads to bigger cell volume. Collectively, these results reveal the “mechanism of adhesion-induced compression of cells,” i.e., stronger interaction between cell and substrate leads to higher actomyosin contractility, expels water and ions, and thus decreases cell volume.     

Micropatterning of single endothelial cell shape reveals a tight coupling between nuclear volume in G1 and proliferation

Shape-dependent local differentials in cell proliferation are considered to be a major driving mechanism of structuring processes in vivo, such as embryogenesis, wound healing, and angiogenesis. However, the specific biophysical signaling by which changes in cell shape contribute to cell cycle regulation remains poorly understood. Here, we describe our study of the roles of nuclear volume and cytoskeletal mechanics in mediating shape control of proliferation in single endothelial cells. Micropatterned adhesive islands were used to independently control cell spreading and elongation. We show that, irrespective of elongation, nuclear volume and apparent chromatin decondensation of cells in G1 systematically increased with cell spreading and highly correlated with DNA synthesis (percent of cells in the S phase). In contrast, cell elongation dramatically affected the organization of the actin cytoskeleton, markedly reduced both cytoskeletal stiffness (measured dorsally with atomic force microscopy) and contractility (measured ventrally with traction microscopy), and increased mechanical anisotropy, without affecting either DNA synthesis or nuclear volume. Our results reveal that the nuclear volume in G1 is predictive of the proliferative status of single endothelial cells within a population, whereas cell stiffness and contractility are not. These findings show that the effects of cell mechanics in shape control of proliferation are far more complex than a linear or straightforward relationship. Our data are consistent with a mechanism by which spreading of cells in G1 partially enhances proliferation by inducing nuclear swelling and decreasing chromatin condensation, thereby rendering DNA more accessible to the replication machinery.