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.     

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.     

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.     

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.     

Cell size and actin architecture determine force generation in optogenetically activated cells

Adherent cells use actomyosin contractility to generate mechanical force and to sense the physical properties of their environment, with dramatic consequences for migration, division, differentiation, and fate. However, the organization of the actomyosin system within cells is highly variable, with its assembly and function being controlled by small GTPases from the Rho family. To understand better how activation of these regulators translates into cell-scale force generation in the context of different physical environments, here we combine recent advances in non-neuronal optogenetics with micropatterning and traction force microscopy on soft elastic substrates. We find that, after whole-cell RhoA activation by the CRY2/CIBN optogenetic system with a short pulse of 100 ms, single cells contract on a minute timescale in proportion to their original traction force, before returning to their original tension setpoint with near perfect precision, on a longer timescale of several minutes. To decouple the biochemical and mechanical elements of this response, we introduce a mathematical model that is parametrized by fits to the dynamics of the substrate deformation energy. We find that the RhoA response builds up quickly on a timescale of 20 s, but decays slowly on a timescale of 50 s. The larger the cells and the more polarized their actin cytoskeleton, the more substrate deformation energy is generated. RhoA activation starts to saturate if optogenetic pulse length exceeds 50 ms, revealing the intrinsic limits of biochemical activation. Together our results suggest that adherent cells establish tensional homeostasis by the RhoA system, but that the setpoint and the dynamics around it are strongly determined by cell size and the architecture of the actin cytoskeleton, which both are controlled by the extracellular environment.     

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.     

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.     

Cell density-dependent decrease in cytoskeletal actin and myosin in cultured osteoblastic cells: correlation with cyclic AMP changes.

During bone development, osteoblasts form a contiguous layer along recently deposited osteoid and their morphology changes from fibroblast-like to cuboidal. In culture, similar changes occur with increased cell density. We examined the possible role of cyclic AMP in this process since cyclic AMP was reported to increase in fibroblasts with increased cell density and similar shape changes were seen in response to parathyroid hormone, which also increases cellular cyclic AMP in osteoblastic cells. Osteoblast-enriched rat calvaria cells were seeded at increasing density. The distribution between Triton X-100 extractable and nonextractable actin and myosin was estimated by polyacrylamide gel electrophoresis. Intracellular cyclic AMP was estimated by prelabeling the cellular ATP pool with 3H-adenine, followed by extraction and separation of 3H-cAMP by high-performance liquid chromatography. We found that osteoblastic cells contain about 40 pg actin and 5.3 pg myosin per cell. Around 60% of the actin and 70% of the myosin were in the nonextractable (crosslinked) form at cell densities of 10,000 to 50,000 cells per cm2. Above 50,000 cells/cm2, there was a cell density-dependent reduction in crosslinked actin and myosin and a concomitant increase in cellular cyclic AMP. A comparable rise in cyclic AMP, produced by incubation with phosphodiesterase inhibitors, and treatment with other agents that increase cyclic AMP produced a similar decrease in the level of cytoskeletal actin and myosin. Cytochalasin B treatment, through its effect on actin polymerization, produced similar changes in cell shape and cytoskeletal actin. The findings suggest that an elevation in intracellular cyclic AMP may play a role in the density-dependent changes in cell shape and microfilament organization observed in osteoblasts.     

Complexity of the tensegrity structure for dynamic energy and force distribution of cytoskeleton during cell spreading

Cytoskeleton plays important roles in intracellular force equilibrium and extracellular force transmission from/to attaching substrate through focal adhesions (FAs). Numerical simulations of intracellular force distribution to describe dynamic cell behaviors are still limited. The tensegrity structure comprises tension-supporting cables and compression-supporting struts that represent the actin filament and microtubule respectively, and has many features consistent with living cells. To simulate the dynamics of intracellular force distribution and total stored energy during cell spreading, the present study employed different complexities of the tensegrity structures by using octahedron tensegrity (OT) and cuboctahedron tensegrity (COT). The spreading was simulated by assigning specific connection nodes for radial displacement and attachment to substrate to form FAs. The traction force on each FA was estimated by summarizing the force carried in sounding cytoskeletal elements. The OT structure consisted of 24 cables and 6 struts and had limitations soon after the beginning of spreading by declining energy stored in struts indicating the abolishment of compression in microtubules. The COT structure, double the amount of cables and struts than the OT structure, provided sufficient spreading area and expressed similar features with documented cell behaviors. The traction force pointed inward on peripheral FAs in the spread out COT structure. The complex structure in COT provided further investigation of various FA number during different spreading stages. Before the middle phase of spreading (half of maximum spreading area), cell attachment with 8 FAs obtained minimized cytoskeletal energy. The maximum number of 12 FAs in the COT structure was required to achieve further spreading. The stored energy in actin filaments increased as cells spread out, while the energy stored in microtubules increased at initial spreading, peaked in middle phase, and then declined as cells reached maximum spreading. The dynamic flows of energy in struts imply that microtubules contribute to structure stabilization.     

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.     

Computational model predicts cell orientation in response to a range of mechanical stimuli

To build anisotropic, mechanically functioning tissue, it is essential to understand how cells orient in response to mechanical stimuli. Therefore, a computational model was developed which predicts cell orientation, based on the actin stress fiber distribution inside the cell. In the model, the stress fiber distribution evolves dynamically according to the following: (1) Stress fibers contain polymerized actin. The total amount of depolymerized plus polymerized actin is constant. (2) Stress fibers apply tension to their environment. This active tension is maximal when strain rate and absolute strain are zero and reduces with increasing shortening rate and absolute strain. (3) A high active fiber stress in a direction leads to a large amount of fibers in this direction. (4) The cell is attached to a substrate; all fiber stresses are homogenized into a total cell stress, which is in equilibrium with substrate stress. This model predicts that on a substrate of anisotropic stiffness, fibers align in the stiffest direction. Under cyclic strain when the cellular environment is so stiff that no compaction occurs (1 MPa), the model predicts strain avoidance, which is more pronounced with increasing strain frequency or amplitude. Under cyclic strain when the cellular environment is so soft that cells can compact it (10 kPa), the model predicts a preference for the cyclically strained compared to the compacting direction. These model predictions all agree with experimental evidence. For the first time, a computational model predicts cell orientation in response to this range of mechanical stimuli using a single set of parameters.     

Toward single cell traction microscopy within 3D collagen matrices

Mechanical interaction between the cell and its extracellular matrix (ECM) regulates cellular behaviors, including proliferation, differentiation, adhesion, and migration. Cells require the three-dimensional (3D) architectural support of the ECM to perform physiologically realistic functions. However, current understanding of cell–ECM and cell–cell mechanical interactions is largely derived from 2D cell traction force microscopy, in which cells are cultured on a flat substrate. 3D cell traction microscopy is emerging for mapping traction fields of single animal cells embedded in either synthetic or natively derived fibrous gels. We discuss here the development of 3D cell traction microscopy, its current limitations, and perspectives on the future of this technology. Emphasis is placed on strategies for applying 3D cell traction microscopy to individual tumor cell migration within collagen gels.     

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

Abstract

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

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.     

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.     

Cell shape regulates collagen type I expression in human tendon fibroblasts

Understanding the relationship between cell shape and cellular function is important for study of cell biology in general and for regulation of cell phenotype in tissue engineering in particular. In this study, microcontact printing technique was used to create cell-adhesive rectangular and circular islands. The rectangular islands had three aspect ratios: 19.6, 4.9, and 2.2, respectively, whereas circular islands had a diameter of 50 microm. Both rectangular and circular islands had the same area of 1960 microm(2). In culture, we found that human tendon fibroblasts (HTFs) assumed the shapes of these islands. Quantitative immunofluorescence measurement showed that more elongated cells expressed higher collagen type I than did less stretched cells even though cell spreading area was the same. This suggests that HTFs, which assume an elongated shape in vivo, have optimal morphology in terms of expression of collagen type I, which is a major component of normal tendons. Using immunohistochemistry along with cell traction force microscopy (CTFM), we further found that these HTFs with different shapes exhibited variations in actin cytoskeletal structure, spatial arrangement of focal adhesions, and spatial distribution and magnitude of cell traction forces. The changes in the actin cytoskeletal structure, focal adhesion distributions, and traction forces in cells with different shapes may be responsible for altered collagen expression, as they are known to be involved in cellular mechanotransduction.     

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

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

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.