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.     

Model-based Traction Force Microscopy Reveals Differential Tension in Cellular Actin Bundles

Adherent cells use forces at the cell-substrate interface to sense and respond to the physical properties of their environment. These cell forces can be measured with traction force microscopy which inverts the equations of elasticity theory to calculate them from the deformations of soft polymer substrates. We introduce a new type of traction force microscopy that in contrast to traditional methods uses additional image data for cytoskeleton and adhesion structures and a biophysical model to improve the robustness of the inverse procedure and abolishes the need for regularization. We use this method to demonstrate that ventral stress fibers of U2OS-cells are typically under higher mechanical tension than dorsal stress fibers or transverse arcs.     

Dynamics of Cell Shape and Forces on Micropatterned Substrates Predicted by a Cellular Potts Model

Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft elastic substrates. To predict the dynamics and steady states of cell shape and forces without any a priori knowledge of how the cell will spread on a given micropattern, here we extend earlier formulations of the two-dimensional cellular Potts model. The third dimension is treated as an area reservoir for spreading. To account for local contour reinforcement by peripheral bundles, we augment the cellular Potts model by elements of the tension-elasticity model. We first parameterize our model and show that it accounts for momentum conservation. We then demonstrate that it is in good agreement with experimental data for shape, spreading dynamics, and traction force patterns of cells on micropatterned substrates. We finally predict shapes and forces for micropatterns that have not yet been experimentally studied.     

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.     

Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions

The interactions between biochemical processes and mechanical signaling play important roles during various cellular processes such as wound healing, embryogenesis, metastasis, and cell migration. While traditional traction force measurements have provided quantitative information about cell matrix interactions in two dimensions, recent studies have shown significant differences in the behavior and morphology of cells when placed in three-dimensional environments. Hence new quantitative experimental techniques are needed to accurately determine cell traction forces in three dimensions. Recently, two approaches both based on laser scanning confocal microscopy have emerged to address this need. This study highlights the details, implementation and advantages of such a three-dimensional imaging methodology with the capability to compute cellular traction forces dynamically during cell migration and locomotion. An application of this newly developed three-dimensional traction force microscopy (3D TFM) technique to single cell migration studies of 3T3 fibroblasts is presented to show that this methodology offers a new quantitative vantage point to investigate the three-dimensional nature of cell-ECM interactions.     

Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics

Cells change their form and function by assembling actin stress fibers at their base and exerting traction forces on their extracellular matrix (ECM) adhesions. Individual stress fibers are thought to be actively tensed by the action of actomyosin motors and to function as elastic cables that structurally reinforce the basal portion of the cytoskeleton; however, these principles have not been directly tested in living cells, and their significance for overall cell shape control is poorly understood. Here we combine a laser nanoscissor, traction force microscopy, and fluorescence photobleaching methods to confirm that stress fibers in living cells behave as viscoelastic cables that are tensed through the action of actomyosin motors, to quantify their retraction kinetics in situ, and to explore their contribution to overall mechanical stability of the cell and interconnected ECM. These studies reveal that viscoelastic recoil of individual stress fibers after laser severing is partially slowed by inhibition of Rho-associated kinase and virtually abolished by direct inhibition of myosin light chain kinase. Importantly, cells cultured on stiff ECM substrates can tolerate disruption of multiple stress fibers with negligible overall change in cell shape, whereas disruption of a single stress fiber in cells anchored to compliant ECM substrates compromises the entire cellular force balance, induces cytoskeletal rearrangements, and produces ECM retraction many microns away from the site of incision; this results in large-scale changes of cell shape (> 5% elongation). In addition to revealing fundamental insight into the mechanical properties and cell shape contributions of individual stress fibers and confirming that the ECM is effectively a physical extension of the cell and cytoskeleton, the technologies described here offer a novel approach to spatially map the cytoskeletal mechanics of living cells on the nanoscale.     

Strength Dependence of Cadherin-Mediated Adhesions

Traction forces between adhesive cells play an important role in a number of collective cell processes. Intercellular contacts, in particular cadherin-based intercellular junctions, are the major means of transmitting force within tissues. We investigated the effect of cellular tension on the formation of cadherin-cadherin contacts by spreading cells on substrates with tunable stiffness coated with N-cadherin homophilic ligands. On the most rigid substrates, cells appear well-spread and present cadherin adhesions and cytoskeletal organization similar to those classically observed on cadherin-coated glass substrates. However, when cells are cultured on softer substrates, a change in morphology is observed: the cells are less spread, with a more disorganized actin network. A quantitative analysis of the cells adhering on the cadherin-coated surfaces shows that forces are correlated with the formation of cadherin adhesions. The stiffer the substrates, the larger are the average traction forces and the more developed are the cadherin adhesions. When cells are treated with blebbistatin to inhibit myosin II, the forces decrease and the cadherin adhesions disappear. Together, these findings are consistent with a mechanosensitive regulation of cadherin-mediated intercellular junctions through the cellular contractile machinery.     

Shear Force at the Cell-Matrix Interface: Enhanced Analysis for Microfabricated Post Array Detectors

The interplay of mechanical forces between the extracellular environment and the cytoskeleton drives development, repair, and senescence in many tissues. Quantitative definition of these forces is a vital step in understanding cellular mechanosensing. Microfabricated post array detectors (mPADs) provide direct measurements of cell-generated forces during cell adhesion to extracellular matrix. A new approach to mPAD post labeling, volumetric imaging, and an analysis of post bending mechanics determined that cells apply shear forces and not point moments at the matrix interface. In addition, these forces could be accurately resolved from post deflections by using images of post tops and bases. Image analysis tools were then developed to increase the precision and throughput of post centroid location. These studies resulted in an improved method of force measurement with broad applicability and concise execution using a fully automated force analysis system. The new method measures cell-generated forces with less than 5% error and less than 90 seconds of computational time. Using this approach, we demonstrated direct and distinct relationships between cellular traction force and spread cell surface area for fibroblasts, endothelial cells, epithelial cells and smooth muscle cells.     

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.     

Dynamic and structural signatures of lamellar actomyosin force generation

The regulation of cellular traction forces on the extracellular matrix is critical to cell adhesion, migration, proliferation, and differentiation. Diverse lamellar actin organizations ranging from contractile lamellar networks to stress fibers are observed in adherent cells. Although lamellar organization is thought to reflect the extent of cellular force generation, understanding of the physical behaviors of the lamellar actin cytoskeleton is lacking. To elucidate these properties, we visualized the actomyosin dynamics and organization in U2OS cells over a broad range of forces. At low forces, contractile lamellar networks predominate and force generation is strongly correlated to actomyosin retrograde flow dynamics with nominal change in organization. Lamellar networks build ～60% of cellular tension over rapid time scales. At high forces, reorganization of the lamellar network into stress fibers results in moderate changes in cellular tension over slower time scales. As stress fibers build and tension increases, myosin band spacing decreases and α-actinin bands form. On soft matrices, force generation by lamellar networks is unaffected, whereas tension-dependent stress fiber assembly is abrogated. These data elucidate the dynamic and structural signatures of the actomyosin cytoskeleton at different levels of tension and set a foundation for quantitative models of cell and tissue mechanics.     

Traction Force Screening Enabled by Compliant PDMS Elastomers

Actomyosin contractility is an essential element of many aspects of cellular biology and manifests as traction forces that cells exert on their surroundings. The central role of these forces makes them a novel principal therapeutic target in diverse diseases. This requires accurate and higher-capacity measurements of traction forces; however, existing methods are largely low throughput, limiting their utility in broader applications. To address this need, we employ Fourier-transform traction force microscopy in a parallelized 96-well format, which we refer to as contractile force screening. Critically, rather than the frequently employed hydrogel polyacrylamide, we fabricate these plates using polydimethylsiloxane rubber. Key to this approach is that the polydimethylsiloxane used is very compliant, with a lower-bound Young’s modulus of ～0.4 kPa. We subdivide these monolithic substrates spatially into biochemically independent wells, creating a uniform multiwell platform for traction force screening. We demonstrate the utility and versatility of this platform by quantifying the compound and dose-dependent contractility responses of human airway smooth muscle cells and retinal pigment epithelial cells. By directly quantifying the endpoint of therapeutic intent, airway-smooth-muscle contractile force, this approach fills an important methodological void in current screening approaches for bronchodilator drug discovery, and, more generally, in measuring contractile response for a broad range of cell types and pathologies.     

Modelling Biological Gel Contraction by Cells: Mechanocellular Formulation and Cell Traction Force Quantification

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cellular traction stresses increase with increasing metastatic potential

Cancer cells exist in a mechanically and chemically heterogeneous microenvironment which undergoes dynamic changes throughout neoplastic progression. During metastasis, cells from a primary tumor acquire characteristics that enable them to escape from the primary tumor and migrate through the heterogeneous stromal environment to establish secondary tumors. Despite being linked to poor prognosis, there are no direct clinical tests available to diagnose the likelihood of metastasis. Moreover, the physical mechanisms employed by metastatic cancer cells to migrate are poorly understood. Because metastasis of most solid tumors requires cells to exert force to reorganize and navigate through dense stroma, we investigated differences in cellular force generation between metastatic and non-metastatic cells. Using traction force microscopy, we found that in human metastatic breast, prostate and lung cancer cell lines, traction stresses were significantly increased compared to non-metastatic counterparts. This trend was recapitulated in the isogenic MCF10AT series of breast cancer cells. Our data also indicate that increased matrix stiffness and collagen density promote increased traction forces, and that metastatic cells generate higher forces than non-metastatic cells across all matrix properties studied. Additionally, we found that cell spreading for these cell lines has a direct relationship with collagen density, but a biphasic relationship with substrate stiffness, indicating that cell area alone does not dictate the magnitude of traction stress generation. Together, these data suggest that cellular contractile force may play an important role in metastasis, and that the physical properties of the stromal environment may regulate cellular force generation. These findings are critical for understanding the physical mechanisms of metastasis and the role of the extracellular microenvironment in metastatic progression.     

Regulation of SMC traction forces in human aortic thoracic aneurysms

Smooth muscle cells (SMCs) usually express a contractile phenotype in the healthy aorta. However, aortic SMCs have the ability to undergo profound changes in phenotype in response to changes in their extracellular environment, as occurs in ascending thoracic aortic aneurysms (ATAA). Accordingly, there is a pressing need to quantify the mechanobiological effects of these changes at single cell level. To address this need, we applied Traction Force Microscopy (TFM) on 759 cells coming from three primary healthy (AoPrim) human SMC lineages and three primary aneurysmal (AnevPrim) human SMC lineages, from age and gender matched donors. We measured the basal traction forces applied by each of these cells onto compliant hydrogels of different stiffness (4, 8, 12, 25 kPa). Although the range of force generation by SMCs suggested some heterogeneity, we observed that: 1. the traction forces were significantly larger on substrates of larger stiffness; 2. traction forces in AnevPrim were significantly higher than in AoPrim cells. We modelled computationally the dynamic force generation process in SMCs using the motor-clutch model and found that it accounts well for the stiffness-dependent traction forces. The existence of larger traction forces in the AnevPrim SMCs were related to the larger size of cells in these lineages. We conclude that phenotype changes occurring in ATAA, which were previously known to reduce the expression of elongated and contractile SMCs (rendering SMCs less responsive to vasoactive agents), tend also to induce stronger SMCs. Future work aims at understanding the causes of this alteration process in aortic aneurysms.

     

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.     

Focus on time: dynamic imaging reveals stretch-dependent cell relaxation and nuclear deformation

Among the stimuli to which cells are exposed in vivo, it has been shown that tensile deformations induce specific cellular responses in musculoskeletal, cardiovascular, and stromal tissues. However, the early response of cells to sustained substrate-based stretch has remained elusive because of the short timescale at which it occurs. To measure the tensile mechanical properties of adherent cells immediately after the application of substrate deformations, we have developed a dynamic traction force microscopy method that enables subsecond temporal resolution imaging of transient subcellular events. The system employs a novel, to our knowledge, tracking approach with minimal computational overhead to compensate substrate-based, stretch-induced motion/drift of stretched single cells in real time, allowing capture of biophysical phenomena on multiple channels by fluorescent multichannel imaging on a single camera, thus avoiding the need for beam splitting with the associated loss of light. Using this tool, we have characterized the transient subcellular forces and nuclear deformations of single cells immediately after the application of equibiaxial strain. Our experiments reveal significant differences in the cell relaxation dynamics and in the intracellular propagation of force to the nuclear compartment in cells stretched at different strain rates and exposes the need for time control for the correct interpretation of dynamic cell mechanics experiments.     

The role of the cytoskeleton in cellular force generation in 2D and 3D environments

To adhere and migrate, cells generate forces through the cytoskeleton that are transmitted to the surrounding matrix. While cellular force generation has been studied on 2D substrates, less is known about cytoskeletal-mediated traction forces of cells embedded in more in vivo-like 3D matrices. Recent studies have revealed important differences between the cytoskeletal structure, adhesion, and migration of cells in 2D and 3D. Because the cytoskeleton mediates force, we sought to directly compare the role of the cytoskeleton in modulating cell force in 2D and 3D. MDA-MB-231 cells were treated with agents that perturbed actin, microtubules, or myosin, and analyzed for changes in cytoskeletal organization and force generation in both 2D and 3D. To quantify traction stresses in 2D, traction force microscopy was used; in 3D, force was assessed based on single cell-mediated collagen fibril reorganization imaged using confocal reflectance microscopy. Interestingly, even though previous studies have observed differences in cell behaviors like migration in 2D and 3D, our data indicate that forces generated on 2D substrates correlate with forces within 3D matrices. Disruption of actin, myosin or microtubules in either 2D or 3D microenvironments disrupts cell-generated force. These data suggest that despite differences in cytoskeletal organization in 2D and 3D, actin, microtubules and myosin contribute to contractility and matrix reorganization similarly in both microenvironments.     

Microfabricated post-array-detectors (mPADs): an approach to isolate mechanical forces

In this video, we will present our approach to measure cellular traction forces using a microfabricated array of posts. Traction forces are generated through myosin-actin interactions and play an important role in our physiology. During development, they enable cells to move from one location to the next in order to form the early structures of tissue. Traction forces help in the healing processes. They are necessary for the proper closure of wounds or the migration and crawling of leukocytes through our body. These same forces can be detrimental to our health in the case of cancer metastasis or vascular growth towards a tumor. The most common method by which to study cells in vitro has been to use a glass or polystyrene dish. However, the rigidity of the substrates makes it impossible to physically measure cell traction forces, and there are relatively few methods to study traction forces. Our lab has developed a technique to overcome these limitations. The method is based on a vertical array of flexible cantilevers, the stiffness and size scale of which are such that individual cells spread across many cantilevers and deflect them in the process. The pillars we use are 3 microm in diameter, 10 microm tall, and are configured in a regular array with 9 microm center-to-center spacing. But these physical dimensions can be readily varied to accommodate a variety of studies. We start with a silicon master, but the final posts are made out of silicone rubber called poly (dimethyl siloxane), or PDMS. We can measure the deflections under a microscope and calculate the magnitude and direction of traction forces required to produce the observed deflections. We call these substrates microfabricated post-array-detectors, or mPADs. Here, we will show you how we fabricate and use the mPADs to assess modulations of cellular contractility.     

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 genetic strategy for the dynamic and graded control of cell mechanics, motility, and matrix remodeling

Cellular mechanical properties have emerged as central regulators of many critical cell behaviors, including proliferation, motility, and differentiation. Although investigators have developed numerous techniques to influence these properties indirectly by engineering the extracellular matrix (ECM), relatively few tools are available to directly engineer the cells themselves. Here we present a genetic strategy for obtaining graded, dynamic control over cellular mechanical properties by regulating the expression of mutant mechanotransductive proteins from a single copy of a gene placed under a repressible promoter. With the use of constitutively active mutants of RhoA GTPase and myosin light chain kinase, we show that varying the expression level of either protein produces graded changes in stress fiber assembly, traction force generation, cellular stiffness, and migration speed. Using this approach, we demonstrate that soft ECMs render cells maximally sensitive to changes in RhoA activity, and that by modulating the ability of cells to engage and contract soft ECMs, we can dynamically control cell spreading, migration, and matrix remodeling. Thus, in addition to providing quantitative relationships between mechanotransductive signaling, cellular mechanical properties, and dynamic cell behaviors, this strategy enables us to control the physical interactions between cells and the ECM and thereby dictate how cells respond to matrix properties.