Traction forces and rigidity sensing regulate cell functions

Ghibaudo, Marion; Saez, Alexandre; Trichet, Léa; Xayaphoummine, A.; Browaeys, Julien; Silberzan, Pascal; Buguin, Axel; Ladoux, Benoît

doi:10.1039/b804103b

Cited by 365 publications

(421 citation statements)

References 50 publications

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“…At later times, cell traction forces on large areas (or at the whole cell level) have also been reported to increase with substrate stiffness as well (9,29,30). This contrasts with the constant stress observed here for 2-μm pillars and shows that initial rigidity sensing events are clearly distinct from later adaptive responses to substrate rigidity.…”

Section: Discussioncontrasting

confidence: 55%

“…Arrays of elastomeric micropillars have proven to be a valuable tool in measuring cellular forces: optical microscopy can be used to precisely measure pillar displacement and generate real-time force maps across entire cells (7,8). For example, over the time scale of hours to days, fibroblasts on arrays of 1-and 2-μm diameter pillars generate average displacements on the order of 100 nm independent of the pillar stiffness over a range of 2-130 nN/μm, i.e., the cells respond to rigidity by measuring the force required to produce a constant displacement (9). However, no studies have examined forces during the initial contact between the cell and the substrate, when the first rigiditysensing events take place (10).…”

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confidence: 99%

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Cells test substrate rigidity by local contractions on submicrometer pillars

Ghassemi

Meacci

Liu

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

248

274

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Cell growth and differentiation are critically dependent upon matrix rigidity, yet many aspects of the cellular rigidity-sensing mechanism are not understood. Here, we analyze matrix forces after initial cell-matrix contact, when early rigidity-sensing events occur, using a series of elastomeric pillar arrays with dimensions extending to the submicron scale (2, 1, and 0.5 μm in diameter covering a range of stiffnesses). We observe that the cellular response is fundamentally different on micron-scale and submicron pillars. On 2-μm diameter pillars, adhesions form at the pillar periphery, forces are directed toward the center of the cell, and a constant maximum force is applied independent of stiffness. On 0.5-μm diameter pillars, adhesions form on the pillar tops, and local contractions between neighboring pillars are observed with a maximum displacement of ∼60 nm, independent of stiffness. Because mutants in rigidity sensing show no detectable displacement on 0.5-μm diameter pillars, there is a correlation between local contractions to 60 nm and rigidity sensing. Localization of myosin between submicron pillars demonstrates that submicron scale myosin filaments can cause these local contractions. Finally, submicron pillars can capture many details of cellular force generation that are missed on larger pillars and more closely mimic continuous surfaces.cell mechanics | mechanotransduction | nanofabrication T he rigidity of matrix substrates provides important signals that determine cell growth (1), differentiation (2, 3), adhesion (4), or motility (5), among others. How the cellular motility machinery can sense matrix rigidity is unknown, but the mechanism(s) of rigidity sensing must be constrained by the size of the rigidity sensing machinery and the physical quantity "measured" by the cell (6). Arrays of elastomeric micropillars have proven to be a valuable tool in measuring cellular forces: optical microscopy can be used to precisely measure pillar displacement and generate real-time force maps across entire cells (7, 8). For example, over the time scale of hours to days, fibroblasts on arrays of 1-and 2-μm diameter pillars generate average displacements on the order of 100 nm independent of the pillar stiffness over a range of 2-130 nN/μm, i.e., the cells respond to rigidity by measuring the force required to produce a constant displacement (9). However, no studies have examined forces during the initial contact between the cell and the substrate, when the first rigiditysensing events take place (10). Moreover, in studies of the minimal cell-substrate contact area needed to sense rigidity and assemble adhesions, fibroblasts assembled adhesion contacts at the edges of beads with contact areas of more than ∼1 μm 2 , whereas with submicron beads, adhesion contacts only assembled after force from a rigid laser tweezers was applied (11). Analysis of bead displacement with laser tweezers also suggests that cells measure the force required for local displacements of ∼100 nm to deduce rigidity, i.e., a constant displ...

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Section: Discussioncontrasting

confidence: 55%

mentioning

confidence: 99%

Cells test substrate rigidity by local contractions on submicrometer pillars

Ghassemi

Meacci

Liu

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

248

274

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“…2 a) and a stiffer endothelium also impedes transmigration. Although the modulus of the ECM ðm t Þ has little influence on the resistance force, it has a strong effect on the actomyosin contractile forces: at the same chemomechanical coupling level, a softer ECM induces lower levels of cellular contractile force (21,26,27), which may not be sufficient for the cells to overcome the resistance force. Therefore, it is less likely for the cell to transmigrate when the ECM is soft (Fig.…”

Section: Ecm Stiffness and Gap Size Modulate Nuclear Transmigrationmentioning

confidence: 99%

A Chemomechanical Model for Nuclear Morphology and Stresses during Cell Transendothelial Migration

Cao

Moeendarbary

Isermann

et al. 2016

Biophysical Journal

119

160

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It is now evident that the cell nucleus undergoes dramatic shape changes during important cellular processes such as cell transmigration through extracellular matrix and endothelium. Recent experimental data suggest that during cell transmigration the deformability of the nucleus could be a limiting factor, and the morphological and structural alterations that the nucleus encounters can perturb genomic organization that in turn influences cellular behavior. Despite its importance, a biophysical model that connects the experimentally observed nuclear morphological changes to the underlying biophysical factors during transmigration through small constrictions is still lacking. Here, we developed a universal chemomechanical model that describes nuclear strains and shapes and predicts thresholds for the rupture of the nuclear envelope and for nuclear plastic deformation during transmigration through small constrictions. The model includes actin contraction and cytosolic back pressure that squeeze the nucleus through constrictions and overcome the mechanical resistance from deformation of the nucleus and the constrictions. The nucleus is treated as an elastic shell encompassing a poroelastic material representing the nuclear envelope and inner nucleoplasm, respectively. Tuning the chemomechanical parameters of different components such as cell contractility and nuclear and matrix stiffnesses, our model predicts the lower bounds of constriction size for successful transmigration. Furthermore, treating the chromatin as a plastic material, our model faithfully reproduced the experimentally observed irreversible nuclear deformations after transmigration in lamin-A/C-deficient cells, whereas the wild-type cells show much less plastic deformation. Along with making testable predictions, which are in accord with our experiments and existing literature, our work provides a realistic framework to assess the biophysical modulators of nuclear deformation during cell transmigration.

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“…A number of cells such as fibroblasts, cardiomyocytes, epithelial cells, endothelial cells and smooth muscle cells develop significant contractile forces as part of their physiological function [9][10][11][12]. One important function of cellular forces is to act on the surrounding extracellular matrix (ECM), align the matrix and reorganize tissues as they form and develop.…”

Section: Introductionmentioning

confidence: 99%

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells

Shenoy¹,

Wang²,

Xiao³

2016

Interface Focus.

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We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature.

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Traction forces and rigidity sensing regulate cell functions

Cited by 365 publications

References 50 publications

Cells test substrate rigidity by local contractions on submicrometer pillars

Cells test substrate rigidity by local contractions on submicrometer pillars

A Chemomechanical Model for Nuclear Morphology and Stresses during Cell Transendothelial Migration

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells

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