Friction-controlled traction force in cell adhesion

The force balance between the extracellular microenvironment and the intracellular cytoskeleton controls the cell fate. We report a new (to our knowledge) mechanism of receptor force control in cell adhesion originating from friction between cell adhesion ligands and the supporting substrate. Adherent human endothelial cells have been studied experimentally on polymer substrates noncovalently coated with fluorescent-labeled fibronectin (FN). The cellular traction force correlated with the mobility of FN during cell-driven FN fibrillogenesis. The experimental findings have been explained within a mechanistic two-dimensional model of the load transfer at focal adhesion sites. Myosin motor activity in conjunction with sliding of FN ligands noncovalently coupled to the surface of the polymer substrates is shown to result in a controlled traction force of adherent cells. We conclude that the friction of adhesion ligands on the supporting substrate is important for mechanotransduction and cell development of adherent cells in vitro and in vivo.     

A predictive model of cell traction forces based on cell geometry

Recent work has indicated that the shape and size of a cell can influence how a cell spreads, develops focal adhesions, and exerts forces on the substrate. However, it is unclear how cell shape regulates these events. Here we present a computational model that uses cell shape to predict the magnitude and direction of forces generated by cells. The predicted results are compared to experimentally measured traction forces, and show that the model can predict traction force direction, relative magnitude, and force distribution within the cell using only cell shape as an input. Analysis of the model shows that the magnitude and direction of the traction force at a given point is proportional to the first moment of area about that point in the cell, suggesting that contractile forces within the cell act on the entire cytoskeletal network as a single cohesive unit. Through this model, we demonstrate that intrinsic properties of cell shape can facilitate changes in traction force patterns, independently of heterogeneous mechanical properties or signaling events within the cell.     

A Novel Cell Traction Force Microscopy to Study Multi-Cellular System

Traction forces exerted by adherent cells on their microenvironment can mediate many critical cellular functions. Accurate quantification of these forces is essential for mechanistic understanding of mechanotransduction. However, most existing methods of quantifying cellular forces are limited to single cells in isolation, whereas most physiological processes are inherently multi-cellular in nature where cell-cell and cell-microenvironment interactions determine the emergent properties of cell clusters. In the present study, a robust finite-element-method-based cell traction force microscopy technique is developed to estimate the traction forces produced by multiple isolated cells as well as cell clusters on soft substrates. The method accounts for the finite thickness of the substrate. Hence, cell cluster size can be larger than substrate thickness. The method allows computing the traction field from the substrate displacements within the cells'' and clusters'' boundaries. The displacement data outside these boundaries are not necessary. The utility of the method is demonstrated by computing the traction generated by multiple monkey kidney fibroblasts (MKF) and human colon cancerous (HCT-8) cells in close proximity, as well as by large clusters. It is found that cells act as individual contractile groups within clusters for generating traction. There may be multiple of such groups in the cluster, or the entire cluster may behave a single group. Individual cells do not form dipoles, but serve as a conduit of force (transmission lines) over long distances in the cluster. The cell-cell force can be either tensile or compressive depending on the cell-microenvironment interactions.     

Influence of type I collagen surface density on fibroblast spreading, motility, and contractility

We examine the relationships of three variables (projected area, migration speed, and traction force) at various type I collagen surface densities in a population of fibroblasts. We observe that cell area is initially an increasing function of ligand density, but that above a certain transition level, increases in surface collagen cause cell area to decline. The threshold collagen density that separates these two qualitatively different regimes, approximately 160 molecules/ microm(2), is approximately equal to the cell surface density of integrin molecules. These results suggest a model in which collagen density induces a qualitative transition in the fundamental way that fibroblasts interact with the substrate. At low density, the availability of collagen binding sites is limiting and the cells simply try to flatten as much as possible by pulling on the few available sites as hard as they can. The force per bond under these conditions approaches 100 pN, approximately equal to the force required for rupture of integrin-peptide bonds. In contrast, at high collagen density adhesion, traction force and motility are limited by the availability of free integrins on the cell surface since so many of these receptors are bound to the surface ligand and the force per bond is very low.     

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.     

A novel patterned magnetic micropillar array substrate for analysis of cellular mechanical responses

Traction forces generated at cellular focal adhesions (FAs) play an essential role in regulating various cellular functions. These forces (1–100 nN) can be measured by observing the local displacement of a flexible substrate upon which cells have been plated. Approaches employing this method include using microfabricated arrays of poly(dimethylsiloxane) (PDMS) micropillars that bend by cellular traction forces. A tool capable of applying a force to FAs independently, by actively moving the micropillars, should become a powerful tool to delineate the cellular mechanotransduction mechanisms. Here, we developed a patterned magnetic micropillar array PDMS substrate that can be used for the mechanical stimulation of cellular FAs and the measurement of associated traction forces. The diameter, length, and center-to-center spacing of the micropillars were 3, 9, and 9 µm, respectively. Iron particles were embedded into the micropillars, enabling the pillars to bend in response to an external magnetic field, which also controlled their location on the substrate. Applying a magnetic field of 0.3 T bent the pillars by ∼4 µm and allowed transfer of external forces to the actin cytoskeleton through FAs formed on the pillar top. Using this approach, we investigated the traction force changes in cultured aortic smooth muscle cells (SMCs) after local compressive stimuli to release cell pretension. The mechanical responses of SMCs were roughly classified into two types: almost a half of the cells showed a little decrease of traction force at each pillar following compressive stimulation, although cell area increased significantly; and the rest showed the opposite, with increased forces and a simultaneous decrease in area. The traction forces of SMCs fluctuated markedly during the local compression. The root mean square of traction forces significantly increased during the compression, and returned to the baseline level after its release. These results suggest that the fluctuation of forces may be caused by active reorganization of the actin cytoskeleton and/or its dynamic interaction with myosin molecules. Thus, our magnetic micropillar substrate would be useful in investigating the mechanotransduction mechanisms of cells.     

Coupling traction force patterns and actomyosin wave dynamics reveals mechanics of cell motion

Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte‐like fan‐shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan‐shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate.     

Force transmission in migrating cells

During cell migration, forces generated by the actin cytoskeleton are transmitted through adhesion complexes to the substrate. To investigate the mechanism of force generation and transmission, we analyzed the relationship between actin network velocity and traction forces at the substrate in a model system of persistently migrating fish epidermal keratocytes. Front and lateral sides of the cell exhibited much stronger coupling between actin motion and traction forces than the trailing cell body. Further analysis of the traction–velocity relationship suggested that the force transmission mechanisms were different in different cell regions: at the front, traction was generated by a gripping of the actin network to the substrate, whereas at the sides and back, it was produced by the network’s slipping over the substrate. Treatment with inhibitors of the actin–myosin system demonstrated that the cell body translocation could be powered by either of the two different processes, actomyosin contraction or actin assembly, with the former associated with significantly larger traction forces than the latter.     

Measurements of elastic moduli of silicone gel substrates with a microfluidic device

Thin layers of gels with mechanical properties mimicking animal tissues are widely used to study the rigidity sensing of adherent animal cells and to measure forces applied by cells to their substrate with traction force microscopy. The gels are usually based on polyacrylamide and their elastic modulus is measured with an atomic force microscope (AFM). Here we present a simple microfluidic device that generates high shear stresses in a laminar flow above a gel-coated substrate and apply the device to gels with elastic moduli in a range from 0.4 to 300 kPa that are all prepared by mixing two components of a transparent commercial silicone Sylgard 184. The elastic modulus is measured by tracking beads on the gel surface under a wide-field fluorescence microscope without any other specialized equipment. The measurements have small and simple to estimate errors and their results are confirmed by conventional tensile tests. A master curve is obtained relating the mixing ratios of the two components of Sylgard 184 with the resulting elastic moduli of the gels. The rigidity of the silicone gels is less susceptible to effects from drying, swelling, and aging than polyacrylamide gels and can be easily coated with fluorescent tracer particles and with molecules promoting cellular adhesion. This work can lead to broader use of silicone gels in the cell biology laboratory and to improved repeatability and accuracy of cell traction force microscopy and rigidity sensing experiments.     

Cell traction force and measurement methods

Cell traction forces (CTFs) are crucial to many biological processes such as inflammation, wound healing, angiogenesis, and metastasis. CTFs are generated by actomyosin interactions and actin polymerization and regulated by intracellular proteins such as alpha-smooth muscle actin (α-SMA) and soluble factors such as transforming growth factor-β (TGF-β). Once transmitted to the extracellular matrix (ECM) through stress fibers via focal adhesions, which are assemblies of ECM proteins, transmembrane receptors, and cytoplasmic structural and signaling proteins (e.g., integrins), CTFs direct many cellular functions, including cell migration, ECM organization, and mechanical signal generation. Various methods have been developed over the years to measure CTFs of both populations of cells and of single cells. At present, cell traction force microscopy (CTFM) is among the most efficient and reliable method for determining CTF field of an entire cell spreading on a two-dimensional (2D) substrate surface. There are currently three CTFM methods, each of which is unique in both how displacement field is extracted from images and how CTFs are subsequently estimated. A detailed review and comparison of these methods are presented. Future research should improve CTFM methods such that they can automatically track dynamic CTFs, thereby providing new insights into cell motility in response to altered biological conditions. In addition, research effort should be devoted to developing novel experimental and theoretical methods for determining CTFs in three-dimensional (3D) matrix, which better reflects physiological conditions than 2D substrate used in current CTFM methods.     

A Novel Method for Localizing Reporter Fluorescent Beads Near the Cell Culture Surface for Traction Force Microscopy

PA gels have long been used as a platform to study cell traction forces due to ease of fabrication and the ability to tune their elastic properties. When the substrate is coated with an extracellular matrix protein, cells adhere to the gel and apply forces, causing the gel to deform. The deformation depends on the cell traction and the elastic properties of the gel. If the deformation field of the surface is known, surface traction can be calculated using elasticity theory. Gel deformation is commonly measured by embedding fluorescent marker beads uniformly into the gel. The probes displace as the gel deforms. The probes near the surface of the gel are tracked. The displacements reported by these probes are considered as surface displacements. Their depths from the surface are ignored. This assumption introduces error in traction force evaluations. For precise measurement of cell forces, it is critical for the location of the beads to be known. We have developed a technique that utilizes simple chemistry to confine fluorescent marker beads, 0.1 and 1 µm in diameter, in PA gels, within 1.6 μm of the surface. We coat a coverslip with poly-D-lysine (PDL) and fluorescent beads. PA gel solution is then sandwiched between the coverslip and an adherent surface. The fluorescent beads transfer to the gel solution during curing. After polymerization, the PA gel contains fluorescent beads on a plane close to the gel surface.     

The dynamics and mechanics of endothelial cell spreading

Cell adhesion to extracellular matrix is mediated by receptor-ligand interactions. When a cell first contacts a surface, it spreads, exerting traction forces against the surface and forming new bonds as its contact area expands. Here, we examined the changes in shape, actin polymerization, focal adhesion formation, and traction stress generation that accompany spreading of endothelial cells over a period of several hours. Bovine aortic endothelial cells were plated on polyacrylamide gels derivatized with a peptide containing the integrin binding sequence RGD, and changes in shape and traction force generation were measured. Notably, both the rate and extent of spreading increase with the density of substrate ligand. There are two prominent modes of spreading: at higher surface ligand densities cells tend to spread isotropically, whereas at lower densities of ligand the cells tend to spread anisotropically, by extending pseudopodia randomly distributed along the cell membrane. The extension of pseudopodia is followed by periods of growth in the cell body to interconnect these extensions. These cycles occur at very regular intervals and, furthermore, the extent of pseudopodial extension can be diminished by increasing the ligand density. Measurement of the traction forces exerted by the cell reveals that a cell is capable of exerting significant forces before either notable focal adhesion or stress fiber formation. Moreover, the total magnitude of force exerted by the cell is linearly related to the area of the cell during spreading. This study is the first to monitor the dynamic changes in the cell shape, spreading rate, and forces exerted during the early stages (first several hours) of endothelial cell adhesion.     

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.     

Mechanotransduction of mesenchymal melanoma cell invasion into 3D collagen lattices: Filopod-mediated extension–relaxation cycles and force anisotropy

Mesenchymal cell migration in interstitial tissue is a cyclic process of coordinated leading edge protrusion, adhesive interaction with extracellular matrix (ECM) ligands, cell contraction followed by retraction and movement of the cell rear. During migration through 3D tissue, the force fields generated by moving cells are non-isotropic and polarized between leading and trailing edge, however the integration of protrusion formation, cell–substrate adhesion, traction force generation and cell translocation in time and space remain unclear. Using high-resolution 3D confocal reflectance and fluorescence microscopy in GFP/actin expressing melanoma cells, we here employ time-resolved subcellular coregistration of cell morphology, interaction and alignment of actin-rich protrusions engaged with individual collagen fibrils. Using single fibril displacement as sensitive measure for force generated by the leading edge, we show how a dominant protrusion generates extension–retraction cycles transmitted through multiple actin-rich filopods that move along the scaffold in a hand-over-hand manner. The resulting traction force is oscillatory, occurs in parallel to cell elongation and, with maximum elongation reached, is followed by rear retraction and movement of the cell body. Combined live-cell fluorescence and reflection microscopy of the leading edge thus reveals step-wise caterpillar-like extension–retraction cycles that underlie mesenchymal migration in 3D tissue.     

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.     

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.     

Cell Migration and Cell-Cell Interaction in the Presence of Mechano-Chemo-Thermotaxis

Although there are several computational models that explain the trajectory that cells take during migration, till now little attention has been paid to the integration of the cell migration in a multi-signaling system. With that aim, a generalized model of cell migration and cell-cell interaction under multisignal environments is presented herein. In this work we investigate the spatio-temporal cell-cell interaction problem induced by mechano-chemo-thermotactic cues. It is assumed that formation of a new focal adhesion generates traction forces proportional to the stresses transmitted by the cell to the extracellular matrix. The cell velocity and polarization direction are calculated based on the equilibrium of the effective forces associated to cell motility. It is also assumed that, in addition to mechanotaxis signals, chemotactic and thermotactic cues control the direction of the resultant traction force. This model enables predicting the trajectory of migrating cells as well as the spatial and temporal distributions of the net traction force and cell velocity. Results indicate that the tendency of the cells is firstly to reach each other and then migrate towards an imaginary equilibrium plane located near the source of the signal. The position of this plane is sensitive to the gradient slope and the corresponding efficient factors. The cells come into contact and separate several times during migration. Adding other cues to the substrate (such as chemotaxis and/or thermotaxis) delays that primary contact. Moreover, in all states, the average local velocity and the net traction force of the cells decrease while the cells approach the cues source. Our findings are qualitatively consistent with experimental observations reported in the related literature.     

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.     

Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts

Mechanical interactions between cell and substrate are involved in vital cellular functions from migration to signal transduction. A newly developed technique, traction force microscopy, makes it possible to visualize the dynamic characteristics of mechanical forces exerted by fibroblasts, including the magnitude, direction, and shear. In the present study such analysis is applied to migrating normal and transformed 3T3 cells. For normal cells, the lamellipodium provides almost all the forces for forward locomotion. A zone of high shear separates the lamellipodium from the cell body, suggesting that they are mechanically distinct entities. Timing and distribution of tractions at the leading edge bear no apparent relationship to local protrusive activities. However, changes in the pattern of traction forces often precede changes in the direction of migration. These observations suggest a frontal towing mechanism for cell migration, where dynamic traction forces at the leading edge actively pull the cell body forward. For H-ras transformed cells, pockets of weak, transient traction scatter among small pseudopods and appear to act against one another. The shear pattern suggests multiple disorganized mechanical domains. The weak, poorly coordinated traction forces, coupled with weak cell-substrate adhesions, are likely responsible for the abnormal motile behavior of H-ras transformed cells.