Tensional Homeostasis in Single Fibroblasts

Adherent cells generate forces through acto-myosin contraction to move, change shape, and sense the mechanical properties of their environment. They are thought to maintain defined levels of tension with their surroundings despite mechanical perturbations that could change tension, a concept known as tensional homeostasis. Misregulation of tensional homeostasis has been proposed to drive disorganization of tissues and promote progression of diseases such as cancer. However, whether tensional homeostasis operates at the single cell level is unclear. Here, we directly test the ability of single fibroblast cells to regulate tension when subjected to mechanical displacements in the absence of changes to spread area or substrate elasticity. We use a feedback-controlled atomic force microscope to measure and modulate forces and displacements of individual contracting cells as they spread on a fibronectin-patterned atomic-force microscope cantilever and coverslip. We find that the cells reach a steady-state contraction force and height that is insensitive to stiffness changes as they fill the micropatterned areas. Rather than maintaining a constant tension, the fibroblasts altered their contraction force in response to mechanical displacement in a strain-rate-dependent manner, leading to a new and stable steady-state force and height. This response is influenced by overexpression of the actin crosslinker α-actinin, and rheology measurements reveal that changes in cell elasticity are also strain- rate-dependent. Our finding of tensional buffering, rather than homeostasis, allows cells to transition between different tensional states depending on how they are displaced, permitting distinct responses to slow deformations during tissue growth and rapid deformations associated with injury.     

Tensional Homeostasis in Single Fibroblasts

Adherent cells generate forces through acto-myosin contraction to move, change shape, and sense the mechanical properties of their environment. They are thought to maintain defined levels of tension with their surroundings despite mechanical perturbations that could change tension, a concept known as tensional homeostasis. Misregulation of tensional homeostasis has been proposed to drive disorganization of tissues and promote progression of diseases such as cancer. However, whether tensional homeostasis operates at the single cell level is unclear. Here, we directly test the ability of single fibroblast cells to regulate tension when subjected to mechanical displacements in the absence of changes to spread area or substrate elasticity. We use a feedback-controlled atomic force microscope to measure and modulate forces and displacements of individual contracting cells as they spread on a fibronectin-patterned atomic-force microscope cantilever and coverslip. We find that the cells reach a steady-state contraction force and height that is insensitive to stiffness changes as they fill the micropatterned areas. Rather than maintaining a constant tension, the fibroblasts altered their contraction force in response to mechanical displacement in a strain-rate-dependent manner, leading to a new and stable steady-state force and height. This response is influenced by overexpression of the actin crosslinker α-actinin, and rheology measurements reveal that changes in cell elasticity are also strain- rate-dependent. Our finding of tensional buffering, rather than homeostasis, allows cells to transition between different tensional states depending on how they are displaced, permitting distinct responses to slow deformations during tissue growth and rapid deformations associated with injury.     

Role of Mechanical Cues in Cell Differentiation and Proliferation: A 3D Numerical Model

Cell differentiation, proliferation and migration are essential processes in tissue regeneration. Experimental evidence confirms that cell differentiation or proliferation can be regulated according to the extracellular matrix stiffness. For instance, mesenchymal stem cells (MSCs) can differentiate to neuroblast, chondrocyte or osteoblast within matrices mimicking the stiffness of their native substrate. However, the precise mechanisms by which the substrate stiffness governs cell differentiation or proliferation are not well known. Therefore, a mechano-sensing computational model is here developed to elucidate how substrate stiffness regulates cell differentiation and/or proliferation during cell migration. In agreement with experimental observations, it is assumed that internal deformation of the cell (a mechanical signal) together with the cell maturation state directly coordinates cell differentiation and/or proliferation. Our findings indicate that MSC differentiation to neurogenic, chondrogenic or osteogenic lineage specifications occurs within soft (0.1-1 kPa), intermediate (20-25 kPa) or hard (30-45 kPa) substrates, respectively. These results are consistent with well-known experimental observations. Remarkably, when a MSC differentiate to a compatible phenotype, the average net traction force depends on the substrate stiffness in such a way that it might increase in intermediate and hard substrates but it would reduce in a soft matrix. However, in all cases the average net traction force considerably increases at the instant of cell proliferation because of cell-cell interaction. Moreover cell differentiation and proliferation accelerate with increasing substrate stiffness due to the decrease in the cell maturation time. Thus, the model provides insights to explain the hypothesis that substrate stiffness plays a key role in regulating cell fate during mechanotaxis.     

Traction force microscopy by deep learning

Cells interact mechanically with their surroundings by exerting and sensing forces. Traction force microscopy (TFM), purported to map cell-generated forces or stresses, represents an important tool that has powered the rapid advances in mechanobiology. However, to solve the ill-posed mathematical problem, conventional TFM involved compromises in accuracy and/or resolution. Here, we applied neural network-based deep learning as an alternative approach for TFM. We modified a neural network designed for image processing to predict the vector field of stress from displacements. Furthermore, we adapted a mathematical model for cell migration to generate large sets of simulated stresses and displacements for training and testing the neural network. We found that deep learning-based TFM yielded results that resemble those using conventional TFM but at a higher accuracy than several conventional implementations tested. In addition, a trained neural network is appliable to a wide range of conditions, including cell size, shape, substrate stiffness, and traction output. The performance of deep learning-based TFM makes it an appealing alternative to conventional methods for characterizing mechanical interactions between adherent cells and the environment.     

Unified multiscale theory of cellular mechanical adaptations to substrate stiffness

Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.     

Orientations of Cells on Compliant Substrates under Biaxial Stretches: A Theoretical Study

Mechanical cues from the microenvironments play a regulating role in many physiological and pathological processes, such as stem cell differentiation and cancer cell metastasis. Experiments showed that cells adhered on a compliant substrate may change orientation with an externally applied strain in the substrate. By accounting for actin polymerization, actin retrograde flow, and integrin binding dynamics, here we develop a mechanism-based tensegrity model to study the orientations of polarized cells on a compliant substrate under biaxial stretches. We show that the cell can actively regulate its mechanical state by generating different traction force levels along its polarized direction. Under static or ultralow-frequency cyclic stretches, stretching a softer substrate leads to a higher increase in the traction force and induces a narrower distribution of cell alignment. Compared to static loadings, high-frequency cyclic loadings have a more significant influence on cell reorientation on a stiff substrate. In addition, the width of the cellular angular distribution scales inversely with the stretch amplitude under both static and cyclic stretches. Our results are in agreement with a wide range of experimental observations, and provide fundamental insights into the functioning of cellular mechanosensing systems.     

High Resolution,Large Deformation 3D Traction Force Microscopy

Traction Force Microscopy (TFM) is a powerful approach for quantifying cell-material interactions that over the last two decades has contributed significantly to our understanding of cellular mechanosensing and mechanotransduction. In addition, recent advances in three-dimensional (3D) imaging and traction force analysis (3D TFM) have highlighted the significance of the third dimension in influencing various cellular processes. Yet irrespective of dimensionality, almost all TFM approaches have relied on a linear elastic theory framework to calculate cell surface tractions. Here we present a new high resolution 3D TFM algorithm which utilizes a large deformation formulation to quantify cellular displacement fields with unprecedented resolution. The results feature some of the first experimental evidence that cells are indeed capable of exerting large material deformations, which require the formulation of a new theoretical TFM framework to accurately calculate the traction forces. Based on our previous 3D TFM technique, we reformulate our approach to accurately account for large material deformation and quantitatively contrast and compare both linear and large deformation frameworks as a function of the applied cell deformation. Particular attention is paid in estimating the accuracy penalty associated with utilizing a traditional linear elastic approach in the presence of large deformation gradients.     

Traction Force Measurements of Human Aortic Smooth Muscle Cells Reveal a Motor-Clutch Behavior

The contractile behavior of smooth muscle cells (SMCs) in the aorta is an important determinant of growth, remodeling, and homeostasis. However, quantitative values of SMC basal tone have never been characterized precisely on individual SMCs. Therefore, to address this lack, we developed an in vitro technique based on Traction Force Microscopy (TFM). Aortic SMCs from a human lineage at low passages (4-7) were cultured 2 days in conditions promoting the development of their contractile apparatus and seeded on hydrogels of varying elastic modulus (1, 4, 12 and 25 kPa) with embedded fluorescent microspheres. After complete adhesion, SMCs were artificially detached from the gel by trypsin treatment. The microbeads movement was tracked and the deformation fields were processed with a mechanical model, assuming linear elasticity, isotropic material, plane strain, to extract the traction forces formerly applied by individual SMCs on the gel. Two major interesting and original observations about SMC traction forces were deduced from the obtained results: 1. they are variable but driven by cell dynamics and show an exponential distribution, with 40% to 80% of traction forces in the range 0-10 μN. 2. They depend on the substrate stiffness: the fraction of adhesion forces below 10 μN tend to decrease when the substrate stiffness increases, whereas the fraction of higher adhesion forces increases. As these two aspects of cell adhesion (variability and stiffness dependence) and the distribution of their traction forces can be predicted by the probabilistic motor-clutch model, we conclude that this model could be applied to SMCs. Further studies will consider stimulated contractility and primary culture of cells extracted from aneurysmal human aortic tissue.     

Fibroblast polarization is a matrix-rigidity-dependent process controlled by focal adhesion mechanosensing

Cell elongation and polarization are basic morphogenetic responses to extracellular matrix adhesion. We demonstrate here that human cultured fibroblasts readily polarize when plated on rigid, but not on compliant, substrates. On rigid surfaces, large and uniformly oriented focal adhesions are formed, whereas cells plated on compliant substrates form numerous small and radially oriented adhesions. Live-cell monitoring showed that focal adhesion alignment precedes the overall elongation of the cell, indicating that focal adhesion orientation may direct cell polarization. siRNA-mediated knockdown of 85 human protein tyrosine kinases (PTKs) induced distinct alterations in the cell polarization response, as well as diverse changes in cell traction force generation and focal adhesion formation. Remarkably, changes in rigidity-dependent traction force development, or focal adhesion mechanosensing, were consistently accompanied by abnormalities in the cell polarization response. We propose that the different stages of cell polarization are regulated by multiple, PTK-dependent molecular checkpoints that jointly control cell contractility and focal-adhesion-mediated mechanosensing.     

Geometry Regulates Traction Stresses in Adherent Cells

Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell’s mechanical output over a wide range of cell geometries.     

Geometry Regulates Traction Stresses in Adherent Cells

Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell’s mechanical output over a wide range of cell geometries.     

Preparation of Complaint Matrices for Quantifying Cellular Contraction

The regulation of cellular adhesion to the extracellular matrix (ECM) is essential for cell migration and ECM remodeling. Focal adhesions are macromolecular assemblies that couple the contractile F-actin cytoskeleton to the ECM. This connection allows for the transmission of intracellular mechanical forces across the cell membrane to the underlying substrate. Recent work has shown the mechanical properties of the ECM regulate focal adhesion and F-actin morphology as well as numerous physiological processes, including cell differentiation, division, proliferation and migration. Thus, the use of cell culture substrates has become an increasingly prevalent method to precisely control and modulate ECM mechanical properties.To quantify traction forces at focal adhesions in an adherent cell, compliant substrates are used in conjunction with high-resolution imaging and computational techniques in a method termed traction force microscopy (TFM). This technique relies on measurements of the local magnitude and direction of substrate deformations induced by cellular contraction. In combination with high-resolution fluorescence microscopy of fluorescently tagged proteins, it is possible to correlate cytoskeletal organization and remodeling with traction forces.Here we present a detailed experimental protocol for the preparation of two-dimensional, compliant matrices for the purpose of creating a cell culture substrate with a well-characterized, tunable mechanical stiffness, which is suitable for measuring cellular contraction. These protocols include the fabrication of polyacrylamide hydrogels, coating of ECM proteins on such gels, plating cells on gels, and high-resolution confocal microscopy using a perfusion chamber. Additionally, we provide a representative sample of data demonstrating location and magnitude of cellular forces using cited TFM protocols. Download video file.^{(68M, mov)}     

Determining substrate displacement and cell traction fields--a new approach

This paper presents a new approach for the traction force microscopy (TFM) method which determines traction forces exerted by adherent cells on a thin, elastic polyacrylamide gel embedded with fluorescent microbeads. In this enhanced TFM method, a pattern recognition technique is first applied to match the pair of microbead embedded images before and after deformation, which subsequently provides the displacement field of the elastic substrate. Once the displacement field is obtained, the 3-D finite element method (FEM) is used to compute cell traction forces. The new TFM has been applied to determine traction forces of human tendon fibroblasts. Compared to existing TFM methods, the present method has the following advantages: (1) its displacement field obtained is associated with microbead movements; (2) it considers the finite thickness of the thin polyacrylamide gel and is therefore free from the infinite half-space approximation adopted by existing TFM methods; and (3) its computation procedure for determining cell traction forces is fast.     

Improved-Throughput Traction Microscopy Based on Fluorescence Micropattern for Manual Microscopy

Traction force microscopy (TFM) is a quantitative technique for measuring cellular traction force, which is important in understanding cellular mechanotransduction processes. Traditional TFM has a significant limitation in that it has a low measurement throughput, commonly one per TFM dish, due to a lack of cell position information. To obtain enough cellular traction force data, an onerous workload is required including numerous TFM dish preparations and heavy cell-seeding activities, creating further difficulty in achieving identical experimental conditions among batches. In this paper, we present an improved-throughput TFM method using the well-developed microcontact printing technique and chemical modifications of linking microbeads to the gel surface to address these limitations. Chemically linking the microbeads to the gel surface has no significant influence on cell proliferation, morphology, cytoskeleton, and adhesion. Multiple pairs of force loaded and null force fluorescence images can be easily acquired by means of manual microscope with the aid of a fluorescence micropattern made by microcontact printing. Furthermore, keeping the micropattern separate from cells by using gels effectively eliminates the potential negative effect of the micropattern on the cells. This novel design greatly improves the analysis throughput of traditional TFM from one to at least twenty cells per petri dish without losing unique advantages, including a high spatial resolution of traction measurements. This newly developed method will boost the investigation of cell-matrix mechanical interactions.     

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.     

Tools for studying and modulating (cardiac muscle) cell mechanics and mechanosensing across the scales

Cardiomyocytes generate force for the contraction of the heart to pump blood into the lungs and body. At the same time, they are exquisitely tuned to the mechanical environment and react to e.g. changes in cell and extracellular matrix stiffness or altered stretching due to reduced ejection fraction in heart disease, by adapting their cytoskeleton, force generation and cell mechanics. Both mechanical sensing and cell mechanical adaptations are multiscale processes. Receptor interactions with the extracellular matrix at the nanoscale will lead to clustering of receptors and modification of the cytoskeleton. This in turn alters mechanosensing, force generation, cell and nuclear stiffness and viscoelasticity at the microscale. Further, this affects cell shape, orientation, maturation and tissue integration at the microscale to macroscale. A variety of tools have been developed and adapted to measure cardiomyocyte receptor-ligand interactions and forces or mechanics at the different ranges, resulting in a wealth of new information about cardiomyocyte mechanobiology. Here, we take stock at the different tools for exploring cardiomyocyte mechanosensing and cell mechanics at the different scales from the nanoscale to microscale and macroscale.     

Determinants of Maximal Force Transmission in a Motor-Clutch Model of Cell Traction in a Compliant Microenvironment

The mechanical stiffness of a cell’s environment exerts a strong, but variable, influence on cell behavior and fate. For example, different cell types cultured on compliant substrates have opposite trends of cell migration and traction as a function of substrate stiffness. Here, we describe how a motor-clutch model of cell traction, which exhibits a maximum in traction force with respect to substrate stiffness, may provide a mechanistic basis for understanding how cells are tuned to sense the stiffness of specific microenvironments. We find that the optimal stiffness is generally more sensitive to clutch parameters than to motor parameters, but that single parameter changes are generally only effective over a small range of values. By contrast, dual parameter changes, such as coordinately increasing the numbers of both motors and clutches offer a larger dynamic range for tuning the optimum. The model exhibits distinct regimes: at high substrate stiffness, clutches quickly build force and fail (so-called frictional slippage), whereas at low substrate stiffness, clutches fail spontaneously before the motors can load the substrate appreciably (a second regime of frictional slippage). Between the two extremes, we find the maximum traction force, which occurs when the substrate load-and-fail cycle time equals the expected time for all clutches to bind. At this stiffness, clutches are used to their fullest extent, and motors are therefore resisted to their fullest extent. The analysis suggests that coordinate parameter shifts, such as increasing the numbers of motors and clutches, could underlie tumor progression and collective cell migration.     

Determinants of Maximal Force Transmission in a Motor-Clutch Model of Cell Traction in a Compliant Microenvironment

The mechanical stiffness of a cell’s environment exerts a strong, but variable, influence on cell behavior and fate. For example, different cell types cultured on compliant substrates have opposite trends of cell migration and traction as a function of substrate stiffness. Here, we describe how a motor-clutch model of cell traction, which exhibits a maximum in traction force with respect to substrate stiffness, may provide a mechanistic basis for understanding how cells are tuned to sense the stiffness of specific microenvironments. We find that the optimal stiffness is generally more sensitive to clutch parameters than to motor parameters, but that single parameter changes are generally only effective over a small range of values. By contrast, dual parameter changes, such as coordinately increasing the numbers of both motors and clutches offer a larger dynamic range for tuning the optimum. The model exhibits distinct regimes: at high substrate stiffness, clutches quickly build force and fail (so-called frictional slippage), whereas at low substrate stiffness, clutches fail spontaneously before the motors can load the substrate appreciably (a second regime of frictional slippage). Between the two extremes, we find the maximum traction force, which occurs when the substrate load-and-fail cycle time equals the expected time for all clutches to bind. At this stiffness, clutches are used to their fullest extent, and motors are therefore resisted to their fullest extent. The analysis suggests that coordinate parameter shifts, such as increasing the numbers of motors and clutches, could underlie tumor progression and collective cell migration.     

Cell spread area and traction forces determine myosin-II-based cortex thickness regulation

Actomyosin network under the plasma membrane of cells forms a cortical layer that regulates cellular deformations during different processes. What regulates the cortex? Characterized by its thickness, it is believed to be regulated by actin dynamics, filament-length regulators and myosin motor proteins. However, its regulation by cellular morphology (e.g. cell spread area) or mechanical microenvironment (e.g. substrate stiffness) has remained largely unexplored. In this study, super- and high-resolution imaging of actin in CHO cells demonstrates that at high spread areas (>450 μm²), the cortex is thinner, better separated as layers, and sensitive to deactivation of myosin II motors or reduction of substrate stiffness (and traction forces). In less spread cells (<400 μm²) such perturbations do not elicit a response. Myosin IIA's mechanosensing is limited here due to its lowered actin-bound fraction and higher turnover rate. Cofilin, in line with its competitive inhibitory role, is found to be overexpressed in these cells. To establish the causal relation, we initiate a spread area drop by de-adhesion and find enhanced actin dynamics and fragmentation along with oscillations and increase in thickness. This is more correlated to the reduction of traction forces than the endocytosis-based reduction in cell volume. Cortex thickness control by spread area is also found be true during differentiation of THP-1 monocytes to macrophages. Thus, we propose that spread area regulates cortex and its thickness by traction-based mechanosensing of myosin II.     

Mechanosensitive axon outgrowth mediated by L1-laminin clutch interface

Mechanical properties of the extracellular environment modulate axon outgrowth. Growth cones at the tip of extending axons generate traction force for axon outgrowth by transmitting the force of actin filament retrograde flow, produced by actomyosin contraction and F-actin polymerization, to adhesive substrates through clutch and cell adhesion molecules. A molecular clutch between the actin filament flow and substrate is proposed to contribute to cellular mechanosensing. However, the molecular identity of the clutch interface responsible for mechanosensitive growth cone advance is unknown. We previously reported that mechanical coupling between actin filament retrograde flow and adhesive substrates through the clutch molecule shootin1a and the cell adhesion molecule L1 generates traction force for axon outgrowth and guidance. Here, we show that cultured mouse hippocampal neurons extend longer axons on stiffer substrates under elastic conditions that correspond to the soft brain environments. We demonstrate that this stiffness-dependent axon outgrowth requires actin-adhesion coupling mediated by shootin1a, L1, and laminin on the substrate. Speckle imaging analyses showed that L1 at the growth cone membrane switches between two adhesive states: L1 that is immobilized and that undergoes retrograde movement on the substrate. The duration of the immobilized phase was longer on stiffer substrates; this was accompanied by increases in actin-adhesion coupling and in the traction force exerted on the substrate. These data suggest that the interaction between L1 and laminin is enhanced on stiffer substrates, thereby promoting force generation for axon outgrowth.