Scaling of Traction Forces with the Size of Cohesive Cell Colonies (original) (raw)

Micropatterning tractional forces in living cells

Cell Motility and the Cytoskeleton, 2002

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-m diameter). Smooth muscle cells were plated onto square (50 ϫ 50 m) or circular (25or 50-m 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. Cell Motil. Cytoskeleton 52: 97-106, 2002.

Traction forces exerted by epithelial cell sheets

Journal of Physics: Condensed Matter, 2010

Whereas the adhesion and migration of individual cells have been well described in terms of physical forces, the mechanics of multicellular assemblies is still poorly understood. Here, we study the behavior of epithelial cells cultured on microfabricated substrates designed to measure cell-to-substrate interactions. These substrates are covered by a dense array of flexible micropillars whose deflection enables us to measure traction forces. They are obtained by lithography and soft replica molding. The pillar deflection is measured by video microscopy and images are analyzed with home-made multiple particle tracking software. First, we have characterized the temporal and spatial distributions of traction forces of cellular assemblies of various sizes. The mechanical force balance within epithelial cell sheets shows that the forces exerted by neighboring cells strongly depend on their relative position in the monolayer: the largest deformations are always localized at the edge of the islands of cells in the active areas of cell protrusions. The average traction stress rapidly decreases from its maximum value at the edge but remains much larger than the inherent noise due to the force resolution of our pillar tracking software, indicating an important mechanical activity inside epithelial cell islands. Moreover, these traction forces vary linearly with the rigidity of the substrate over about two decades, suggesting that cells exert a given amount of deformation rather than a force. Finally, we engineer micropatterned substrates supporting pillars with anisotropic stiffness. On such substrates cellular growth is aligned with respect to the stiffest direction in correlation with the magnitude of the applied traction forces.

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

2013

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 displ...

Traction forces and rigidity sensing regulate cell functions

Soft Matter, 2008

Increasing evidence suggests that mechanical cues inherent to the extracellular matrix may be as important as its chemical nature in regulating cell behavior. Here, the response of cells to the mechanical properties of the substrate is examined by culturing 3T3 fibroblastic cells and epithelial cells on surfaces composed of a dense array of flexible microfabricated pillars. We focus on the influence of substrate rigidity on the traction forces exerted by cells, and on cell adhesion and migration. We first measure these forces by monitoring the deflection of the pillars. Then, by varying their geometric parameters, we control the substrate stiffness over a large range from 1 to 200 nN mm À1 . We show that the force-rigidity relationship exhibits a similar behavior for both cell types. Two distinct regimes are evidenced: first, a linear increase of the force with the rigidity and then a saturation plateau for the largest rigidities. We observe that the cell spreading area increases with increasing rigidity, as well as the size of focal adhesions. Substrates with an anisotropic rigidity allow us to determine that the migration paths of 3T3 cells are oriented in the stiffest direction in correlation with maximal traction forces. Finally, to compare the force measurements on micro-textured surfaces and continuous flexible gels, we propose an elastic model that estimates the equivalent Young's modulus of a micropillar substrate. This qualitative model gives comparable results for both experimental approaches.

Tissue pressure and cell traction compensate to drive robust aggregate spreading

2020

In liquid droplets, the balance of interfacial energies and substrate elasticity determines the shape of the droplet and the dynamics of wetting. In living cells, interfacial energies are not constant, but adapt to the mechanics of their environment. As a result, the forces driving the dynamics of wetting for cells and tissues are unclear and may be context specific. In this work, using a combination of experimental measurements and modeling, we show the surface tension of cell aggregates, as models of active liquid droplets, depends upon the size of the aggregate and the magnitude of applied load, which alters the wetting dynamics. Upon wetting rigid substrates, traction stresses are elevated at the boundary, and tension drives forward motion. By contrast, upon wetting compliant substrates, traction forces are attenuated, yet wetting occurs at a comparable rate. In this case, capillary forces at the contact line are elevated and aggregate surface tension contributes to strong outwa...

The regulation of traction force in relation to cell shape and focal adhesions

Biomaterials, 2011

Mechanical forces provide critical inputs for proper cellular functions. The interplay between the generation of, and response to, mechanical forces regulate such cellular processes as differentiation, proliferation, and migration. We postulate that adherent cells respond to a number of physical and topographical factors, including cell size and shape, by detecting the magnitude and/or distribution of traction forces under different conditions. To address this possibility we introduce a new simple method for precise micropatterning of hydrogels, and then apply the technique to systematically investigate the relationship between cell geometry, focal adhesions, and traction forces in cells with a series of spread areas and aspect ratios. Contrary to previous findings, we find that traction force is not determined primarily by the cell spreading area but by the distance from cell center to the perimeter. This distance in turn controls traction forces by regulating the size of focal adhesions, such that constraining the size of focal adhesions by micropatterning can override the effect of geometry. We propose that the responses of traction forces to center-periphery distance, possibly through a positive feedback mechanism that regulates focal adhesions, provide the cell with the information on its own shape and size. A similar positive feedback control may allow cells to respond to a variety of physical or topographical signals via a unified mechanism.

Endogenous Sheet-Averaged Tension Within a Large Epithelial Cell Colony

Journal of Biomechanical Engineering, 2017

Epithelial cells form quasi-two-dimensional sheets that function as contractile media to effect tissue shape changes during development and homeostasis. Endogenously generated intrasheet tension is a driver of such changes, but has predominantly been measured in the presence of directional migration. The nature of epithelial cell-generated forces transmitted over supracellular distances, in the absence of directional migration, is thus largely unclear. In this report, we consider large epithelial cell colonies which are archetypical multicell collectives with extensive cell–cell contacts but with a symmetric (circular) boundary. Using the traction force imbalance method (TFIM) (traction force microscopy combined with physical force balance), we first show that one can determine the colony-level endogenous sheet forces exerted at the midline by one half of the colony on the other half with no prior assumptions on the uniformity of the mechanical properties of the cell sheet. Importan...

Collective cell migration induced by mechanical stress and substrate adhesiveness

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

Mechanical stress normal to the boundary of a tissue sheet can arise in both constrained as well as unconstrained epithelial layers through pushing and pulling of surrounding tissue and substrate adhesiveness, respectively. A continuum model is used to investigate how such stress influences the epithelial dynamics. Four types of spreading and motility can be identified: a uniformly stretched stationary state, uniform sheet migration, active stress compensation by polarization close to the boundary, and a wormlike progression by deformation waves. Analytical and numerical solutions are presented along with bifurcation diagrams using normal stress and active force as control parameters.

Cell-ECM traction force modulates endogenous tension at cell-cell contacts

Proceedings of the National Academy of Sciences, 2011

Cells in tissues are mechanically coupled both to the ECM and neighboring cells, but the coordination and interdependency of forces sustained at cell-ECM and cell-cell adhesions are unknown. In this paper, we demonstrate that the endogenous force sustained at the cell-cell contact between a pair of epithelial cells is approximately 100 nN, directed perpendicular to the cell-cell interface and concentrated at the contact edges. This force is stably maintained over time despite significant fluctuations in cell-cell contact length and cell morphology. A direct relationship between the total cellular traction force on the ECM and the endogenous cell-cell force exists, indicating that the cell-cell tension is a constant fraction of the cell-ECM traction. Thus, modulation of ECM properties that impact cell-ECM traction alters cell-cell tension. Finally, we show in a minimal model of a tissue that all cells experience similar forces from the surrounding microenvironment, despite differences in the extent of cell-ECM and cell-cell adhesion. This interdependence of cell-cell and cell-ECM forces has significant implications for the maintenance of the mechanical integrity of tissues, mechanotransduction, and tumor mechanobiology. cellular mechanotransduction | cadherin | adherens junctions | focal adhesions | intercellular force transmission 4708-4713 | PNAS | March 22, 2011 | vol. 108 | no. 12

Prediction of traction forces of motile cells

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.