Separation of propulsive and adhesive traction stresses in locomoting keratocytes

Strong, actomyosin-dependent, pinching tractions in steadily locomoting (gliding) fish keratocytes revealed by traction imaging present a paradox, since only forces perpendicular to the direction of locomotion are apparent, leaving the actual propulsive forces unresolved. When keratocytes become transiently "stuck" by their trailing edge and adopt a fibroblast-like morphology, the tractions opposing locomotion are concentrated into the tail, leaving the active pinching and propulsive tractions clearly visible under the cell body. Stuck keratocytes can develop approximately 1 mdyn (10,000 pN) total propulsive thrust, originating in the wings of the cell. The leading lamella develops no detectable propulsive traction, even when the cell pulls on its transient tail anchorage. The separation of propulsive and adhesive tractions in the stuck phenotype leads to a mechanically consistent hypothesis that resolves the traction paradox for gliding keratocytes: the propulsive tractions driving locomotion are normally canceled by adhesive tractions resisting locomotion, leaving only the pinching tractions as a resultant. The resolution of the traction pattern into its components specifies conditions to be met for models of cytoskeletal force production, such as the dynamic network contraction model (Svitkina, T.M., A.B. Verkhovsky, K.M. McQuade, and G.G. Borisy. 1997. J. Cell Biol. 139:397-415). The traction pattern associated with cells undergoing sharp turns differs markedly from the normal pinching traction pattern, and can be accounted for by postulating an asymmetry in contractile activity of the opposed lateral wings of the cell.     

Spatial and temporal traction response in human airway smooth muscle cells

Tractions that cells exert on theirsubstrates are essential in cell spreading, migration, and contraction.These tractions can be determined by plating the cells on a flexiblegel and measuring the deformation of the gel by using fluorescent beadsembedded just below the surface of the gel. In this article we describe the image correlation method (ICM) optimized for determining the displacement field of the gel under a contracting cell. For the calculation of the traction field from the displacement field we usethe recently developed method of Fourier transform traction cytometry(FTTC). The ICM and FTTC methods are applied to human airway smoothmuscle cells during stimulation with the contractile agonist histamineor the relaxing agonist isoproterenol. The overall intensity of thecell contraction (the median traction magnitude, the energy transferredfrom the cell to the gel, and the net contractile moment) increasedafter activation with histamine, and decreased after treatment withisoproterenol. Cells exhibited regional differences in the time courseof traction during the treatment. Both temporal evolution and magnitudeof traction increase induced by histamine varied markedly amongdifferent cell protrusions, whereas the nuclear region showed thesmallest response. These results suggest that intracellular mediatorsof cell adhesion and contraction respond to contractile stimuli withdifferent rates and intensities in different regions of the cell.

     

Stresses at the cell-to-substrate interface during locomotion of fibroblasts

Recent technological improvements in the elastic substrate method make it possible to produce spatially resolved measurements of the tractions exerted by single motile cells. In this study we have applied these developments to produce maps of the tractions exerted by 3T3 fibroblasts during steady locomotion. The resulting images have a spatial resolution of approximately 5 micrometers and a maximum intensity of approximately 10(2) kdyn/cm2 (10(4) pN/micrometers2). We find that the propulsive thrust for fibroblast locomotion, approximately 0.2 dyn, is imparted to the substratum within 15 micrometers of the leading edge. These observations demonstrate that the lamellipodium of the fibroblast is able to generate intense traction stress. The cell body and posterior seem to be mechanically passive structures pulled forward entirely by this action.     

Contractile forces in tumor cell migration

Cancer is a deadly disease primarily because of the ability of tumor cells to spread from the primary tumor, to invade into the connective tissue, and to form metastases at distant sites. In contrast to cell migration on a planar surface where large cell tractions and contractile forces are not essential, tractions and forces are thought to be crucial for overcoming the resistance and steric hindrance of a dense three-dimensional connective tissue matrix. In this review, we describe recently developed biophysical tools, including 2-D and 3-D traction microscopy to measure contractile forces of cells. We discuss evidence indicating that tumor cell invasiveness is associated with increased contractile force generation.     

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.     

Finite element analysis of the effects of focal adhesion mechanical properties and substrate stiffness on cell migration

The attachment of cells to the extracellular matrix (ECM) is achieved by the specific binding of cell-surface receptors to ligands present in the ECM. These interactions are important for many biological processes, including cell migration, cancer development, and wound healing. Our objective was to develop a computational model to investigate how focal adhesion mechanical properties, substrate stiffness, and intracellular stresses affect cell-matrix interactions during cell migration on a flat substrate. In our model, the cell-substrate traction was proportional to the bound receptor concentration, relative velocity between the cell and substrate, and the cell-substrate friction coefficient. Simulation results showed that even if the receptor number and ligand density were fixed, the mechanical properties of the focal adhesions still affected cell-ECM interactions. In fact, the cell-substrate traction was biphasic with respect to the friction coefficient, a parameter that can be used to quantify focal adhesion properties. In contrast, the cell speed was a monotonically decreasing function with respect to this parameter. Furthermore, tractions showed greater increases when the maximum intracellular stress was increased from 400 to 600Pa than when substrate stiffness was increased from 0.5 to 100kPa. This mathematical model is able to quantify the effects of focal adhesion mechanical properties, extracellular stiffness, and intracellular stresses on cell-ECM interactions, and should be beneficial to research in cancer development.     

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.     

Cellular traction force recovery: An optimal filtering approach in two-dimensional Fourier space

Quantitative estimation of cellular traction has significant physiological and clinical implications. As an inverse problem, traction force recovery is essentially susceptible to noise in the measured displacement data. For traditional procedure of Fourier transform traction cytometry (FTTC), noise amplification is accompanied in the force reconstruction and small tractions cannot be recovered from the displacement field with low signal-noise ratio (SNR). To improve the FTTC process, we develop an optimal filtering scheme to suppress the noise in the force reconstruction procedure. In the framework of the Wiener filtering theory, four filtering parameters are introduced in two-dimensional Fourier space and their analytical expressions are derived in terms of the minimum-mean-squared-error (MMSE) optimization criterion. The optimal filtering approach is validated with simulations and experimental data associated with the adhesion of single cardiac myocyte to elastic substrate. The results indicate that the proposed method can highly enhance SNR of the recovered forces to reveal tiny tractions in cell-substrate interaction.     

Decoupling Substrate Stiffness, Spread Area, and Micropost Density: A Close Spatial Relationship between Traction Forces and Focal Adhesions

Mechanical cues can influence the manner in which cells generate traction forces and form focal adhesions. The stiffness of a cell's substrate and the available area on which it can spread can influence its generation of traction forces, but to what extent these factors are intertwined is unclear. In this study, we used microcontact printing and micropost arrays to control cell spreading, substrate stiffness, and post density to assess their effect on traction forces and focal adhesions. We find that both the spread area and the substrate stiffness influence traction forces in an independent manner, but these factors have opposite effects: cells on stiffer substrates produce higher average forces, whereas cells with larger spread areas generate lower average forces. We show that post density influences the generation of traction forces in a manner that is more dominant than the effect of spread area. Additionally, we observe that focal adhesions respond to spread area, substrate stiffness, and post density in a manner that closely matches the trends seen for traction forces. This work supports the notion that traction forces and focal adhesions have a close relationship in their response to mechanical cues.     

An array of microfabricated pillars to study cell migration

Mechanical forces play an important role in various cellular functions, such as tumor metastasis, embryonic development or tissue formation. Cell migration involves dynamics of adhesive processes and cytoskeleton remodelling, leading to traction forces between the cells and their surrounding extracellular medium. To study these mechanical forces, a number of methods have been developed to calculate tractions at the interface between the cell and the substrate by tracking the displacements of beads or microfabricated markers embedded in continuous deformable gels. These studies have provided the first reliable estimation of the traction forces under individual migrating cells. We have developed a new force sensor made of a dense array of soft micron-size pillars microfabricated using microelectronics techniques. This approach uses elastomeric substrates that are micropatterned by using a combination of hard and soft lithography. Traction forces are determined in real time by analyzing the deflections of each micropillar with an optical microscope. Indeed, the deflection is directly proportional to the force in the linear regime of small deformations. Epithelial cells are cultured on our substrates coated with extracellular matrix protein. First, we have characterized temporal and spatial distributions of traction forces of a cellular assembly. Forces are found to depend on their relative position in the monolayer : the strongest deformations are always localized at the edge of the islands of cells in the active areas of cell protrusions. Consequently, these forces are quantified and correlated with the adhesion/scattering processes of the cells.     

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.     

Free Form Deformation–Based Image Registration Improves Accuracy of Traction Force Microscopy

Traction Force Microscopy (TFM) is a widespread method used to recover cellular tractions from the deformation that they cause in their surrounding substrate. Particle Image Velocimetry (PIV) is commonly used to quantify the substrate’s deformations, due to its simplicity and efficiency. However, PIV relies on a block-matching scheme that easily underestimates the deformations. This is especially relevant in the case of large, locally non-uniform deformations as those usually found in the vicinity of a cell’s adhesions to the substrate. To overcome these limitations, we formulate the calculation of the deformation of the substrate in TFM as a non-rigid image registration process that warps the image of the unstressed material to match the image of the stressed one. In particular, we propose to use a B-spline -based Free Form Deformation (FFD) algorithm that uses a connected deformable mesh to model a wide range of flexible deformations caused by cellular tractions. Our FFD approach is validated in 3D fields using synthetic (simulated) data as well as with experimental data obtained using isolated endothelial cells lying on a deformable, polyacrylamide substrate. Our results show that FFD outperforms PIV providing a deformation field that allows a better recovery of the magnitude and orientation of tractions. Together, these results demonstrate the added value of the FFD algorithm for improving the accuracy of traction recovery.     

Embryonic Stem Cells Do Not Stiffen on Rigid Substrates

It has been previously established that living cells, including mesenchymal stem cells, stiffen in response to elevation of substrate stiffness. This stiffening is largely attributed to the elevation of the tractions at the cell base that is associated with increases in cell spreading on more-rigid substrates. We show here, surprisingly, that mouse embryonic stem cells (ESCs) do not stiffen when substrate stiffness increases. As shown recently, these cells do not increase spreading on more-rigid substrates either. However, these ESCs do increase their basal tractions as substrate stiffness increases. We conclude that these ESCs exhibit mechanical behaviors distinct from those of mesenchymal stem cells and of terminally differentiated cells, and decouple its apical cell stiffness from its basal tractional stresses during the substrate rigidity response.     

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.     

Nascent focal adhesions are responsible for the generation of strong propulsive forces in migrating fibroblasts

Fibroblast migration involves complex mechanical interactions with the underlying substrate. Although tight substrate contact at focal adhesions has been studied for decades, the role of focal adhesions in force transduction remains unclear. To address this question, we have mapped traction stress generated by fibroblasts expressing green fluorescent protein (GFP)-zyxin. Surprisingly, the overall distribution of focal adhesions only partially resembles the distribution of traction stress. In addition, detailed analysis reveals that the faint, small adhesions near the leading edge transmit strong propulsive tractions, whereas large, bright, mature focal adhesions exert weaker forces. This inverse relationship is unique to the leading edge of motile cells, and is not observed in the trailing edge or in stationary cells. Furthermore, time-lapse analysis indicates that traction forces decrease soon after the appearance of focal adhesions, whereas the size and zyxin concentration increase. As focal adhesions mature, changes in structure, protein content, or phosphorylation may cause the focal adhesion to change its function from the transmission of strong propulsive forces, to a passive anchorage device for maintaining a spread cell morphology.     

Traction patterns of tumor cells

The traction exerted by a cell on a planar deformable substrate can be indirectly obtained on the basis of the displacement field of the underlying layer. The usual methodology used to address this inverse problem is based on the exploitation of the Green tensor of the linear elasticity problem in a half space (Boussinesq problem), coupled with a minimization algorithm under force penalization. A possible alternative strategy is to exploit an adjoint equation, obtained on the basis of a suitable minimization requirement. The resulting system of coupled elliptic partial differential equations is applied here to determine the force field per unit surface generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field and is a promising tool to investigate the spatial pattern of force per unit surface generated in cell motion, particularly in the case of such cancer cells.     

Rho mediates the shear-enhancement of endothelial cell migration and traction force generation

The migration of vascular endothelial cells in vivo occurs in a fluid dynamic environment due to blood flow, but the role of hemodynamic forces in cell migration is not yet completely understood. Here we investigated the effect of shear stress, the frictional drag of blood flowing over the cell surface, on the migration speed of individual endothelial cells on fibronectin-coated surfaces, as well as the biochemical and biophysical bases underlying this shear effect. Under static conditions, cell migration speed had a bell-shaped relationship with fibronectin concentration. Shear stress significantly increased the migration speed at all fibronectin concentrations tested and shifted the bell-shaped curve upwards. Shear stress also induced the activation of Rho GTPase and increased the traction force exerted by endothelial cells on the underlying substrate, both at the leading edge and the rear, suggesting that shear stress enhances both the frontal forward-pulling force and tail retraction. The inhibition of a Rho-associated kinase, p160ROCK, decreased the traction force and migration speed under both static and shear conditions and eliminated the shear-enhancement of migration speed. Our results indicate that shear stress enhances the migration speed of endothelial cells by modulating the biophysical force of tractions through the biochemical pathway of Rho-p160ROCK.     

Micropatterning tractional forces in living cells

Here we describe a method for quantifying traction in cells that are physically constrained within micron-sized adhesive islands of defined shape and size on the surface of flexible polyacrylamide gels that contain fluorescent microbeads (0.2-microm diameter). Smooth muscle cells were plated onto square (50 x 50 microm) or circular (25- or 50-microm diameter) adhesive islands that were created on the surface of the gels by applying a collagen coating through microengineered holes in an elastomeric membrane that was later removed. Adherent cells spread to take on the size and shape of the islands and cell tractions were quantitated by mapping displacement fields of the fluorescent microbeads within the gel. Cells on round islands did not exhibit any preferential direction of force application, but they exerted their strongest traction at sites where they formed protrusions. When cells were confined to squares, traction was highest in the corners both in the absence and presence of the contractile agonist, histamine, and cell protrusions were also observed in these regions. Quantitation of the mean traction exerted by cells cultured on the different islands revealed that cell tension increased as cell spreading was promoted. These results provide a mechanical basis for past studies that demonstrated a similar correlation between spreading and growth within various anchorage-dependent cells. This new approach for analyzing the spatial distribution of mechanical forces beneath individual cells that are experimentally constrained to defined sizes and shapes may provide additional insight into the biophysical basis of cell regulation.     

Guidance of Cell Migration by Substrate Dimension

There is increasing evidence to suggest that physical parameters, including substrate rigidity, topography, and cell geometry, play an important role in cell migration. As there are significant differences in cell behavior when cultured in 1D, 2D, or 3D environments, we hypothesize that migrating cells are also able to sense the dimension of the environment as a guidance cue. NIH 3T3 fibroblasts were cultured on micropatterned substrates where the path of migration alternates between 1D lines and 2D rectangles. We found that 3T3 cells had a clear preference to stay on 2D rather than 1D substrates. Cells on 2D surfaces generated stronger traction stress than did those on 1D surfaces, but inhibition of myosin II caused cells to lose their sensitivity to substrate dimension, suggesting that myosin-II-dependent traction forces are the determining factor for dimension sensing. Furthermore, oncogene-transformed fibroblasts are defective in mechanosensing while generating similar traction forces on 1D and 2D surfaces. Dimension sensing may be involved in guiding cell migration for both physiological functions and tissue engineering, and for maintaining normal cells in their home tissue.     

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.