Early-time dynamics of actomyosin polarization in cells of confined shape in elastic matrices

Mechanical interplay between cell shape and actin cytoskeleton organization

We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses. Upon modeling the actin cytoskeleton as a nematic liquid crystal, we further show that the geometry of the cell edge feeds back on the organization of the stress fibers by altering the length scale at which these are confined. This feedback mechanism is controlled by a dimensionless number, the anchoring number, representing the relative weight of surface-anchoring and bulk-aligning torques. Our model allows to predict both cellular shape and the internal structure of the actin cytoskeleton and is in good quantitative agreement with experiments on fibroblastoid (GDβ1, GDβ3) and epithelioid (GEβ1, GEβ3) cells.

Dynamics of force generation by spreading platelets

In order to gain more insight into the role of human platelets for blood clot formation, here we investigate the dynamics of force generation by platelet spreading onto elastic substrates of variable stiffness. Despite their small size, platelets generate high and rapidly varying traction forces on their extracellular environment, which we reconstruct with adapted implementations of Fourier transform traction cytometry. We find that while the final spread area is reached within a few minutes, the build-up of forces typically takes 10-30 minutes. In addition, we identify two distinct behaviors of individual cells, namely oscillating and non-oscillating platelets. An eigenvalue analysis of the platelet dipole tensor reveals a small anisotropy of the exerted force, which is compatible with a random distribution of a few force transmitting centers, in agreement with the observed shapes and traction patterns. We find a correlation between the maximum force level a platelet reaches and its spread area, which we explain by a thin film model for the actively contracting cell. The model reveals a large internal stress of hundreds of kPa. Experimentally we do not find any statistically relevant relation between the force level reached and the substrate stiffness within the stiffness range from 19 to 83 kPa, which might be related to the high platelet activation level used in our study. In addition, our model suggests that due to the uniquely small thickness of platelets, their mechanosensitivity might be limited to a lower stiffness range.

Theoretical Analysis of Stress Distribution and Cell Polarization Surrounding a Model Wound

A growing amount of experimental evidence shows that the local elastic field acting on cells governs their spatial organization and polarity in a tissue. Interestingly, experiments on wound healing reveal a universal formation of thick actomyosin bundles around the margins of epithelial gaps. Although the forces involved in this process have been measured, the mechanisms governing cellular alignment and contractile ring formation are still not fully understood. To theoretically investigate this process, we have carried out a self-consistent calculation of the elastic field that is actively generated around a circular gap in a contractile cell monolayer that is adhered to an elastic substrate, taking into account the responsiveness of actomyosin activity to the locally generated stress. We model actomyosin contractility by a radial distribution of point force dipoles that may alter in magnitude and orientation in response to the local elastic stress. In addition, the model takes into account the forces exerted by leader cells on the margins of the cell monolayer. Our model suggests that the presence of a hole in the center of a contractile cell monolayer creates a mechanical tendency for actomyosin forces to polarize tangentially around the hole margin. In addition, it predicts that this tendency optimizes with substrate rigidity, thickness, and strength of cell adhesion to the substrate. Our calculations support the view that the universal formation of a peripheral contractile ring is a consequence of actomyosin contractility in the bulk and its inherent responsiveness to the local stress.

Parallel Compression Is a Fast Low-Cost Assay for the High-Throughput Screening of Mechanosensory Cytoskeletal Proteins in Cells

Cellular mechanosensing is critical for many biological processes, including cell differentiation, proliferation, migration, and tissue morphogenesis. The actin cytoskeletal proteins play important roles in cellular mechanosensing. Many techniques have been used to investigate the mechanosensory behaviors of these proteins. However, a fast, low-cost assay for the quantitative characterization of these proteins is still lacking. Here, we demonstrate that compression assay using agarose overlay is suitable for the high throughput screening of mechanosensory proteins in live cells while requiring minimal experimental setup. We used several well-studied myosin II mutants to assess the compression assay. On the basis of elasticity theories, we simulated the mechanosensory accumulation of myosin II's and quantitatively reproduced the experimentally observed protein dynamics. Combining the compression assay with confocal microscopy, we monitored the polarization of myosin II oligomers at the subcellular level. The polarization was dependent on the ratio of the two principal strains of the cellular deformations. Finally, we demonstrated that this technique could be used on the investigation of other mechanosensory proteins.

Dynamics of cell area and force during spreading

Experiments on human pulmonary artery endothelial cells are presented to show that cell area and the force exerted on a substrate increase simultaneously, but with different rates during spreading; rapid-force increase systematically occurred several minutes past initial spreading. We examine this theoretically and present three complementary mechanisms that may accompany the development of lamellar stress during spreading and underlie the observed behavior. These include: 1), the dynamics of cytoskeleton assembly at the cell basis; 2), the strengthening of acto-myosin forces in response to the generated lamellar stresses; and 3), the passive strain-stiffening of the cytoskeleton.

Contribution of myosin II activity to cell spreading dynamics

Myosin II activity and actin polymerization at the leading edge of the cell are known to be essential sources of cellular stress. However, a quantitative account of their separate contributions is still lacking; so is the influence of the coupling between the two phenomena on cell spreading dynamics. We present a simple analytic elastic theory of cell spreading dynamics that quantitatively demonstrates how actin polymerization and myosin activity cooperate in the generation of cellular stress during spreading. Consistent with experiments, myosin activity is assumed to polarize in response to the stresses generated during spreading. The characteristic response time and the overall spreading time are predicted to determine different evolution profiles of cell spreading dynamics. These include, a (regular) monotonic increase of cell projected area with time, a non-monotonic (overshooting) profile with a maximum, and damped oscillatory modes. In addition, two populations of myosin II motors are distinguished based on their location in the lamella; those located above the major adhesion zone at the cell periphery are shown to facilitate spreading whereas those in deeper regions of the lamella are shown to oppose spreading. We demonstrate that the attenuation of myosin activity in the two regions may result in reciprocal effects on spreading. These findings provide important new insight into the function of myosin II motors in the course of spreading.

Active mechanical coupling between the nucleus, cytoskeleton and the extracellular matrix, and the implications for perinuclear actomyosin organization

Experimental and theoretical studies have demonstrated that the polarization of actomyosin forces in the cytoskeleton of adherent cells is governed by local elastic stresses. Based on this phenomenon, and the established observation that the nucleus is mechanically connected to the extracellular matrix (ECM) via the cytoskeleton, we theoretically analyze here the active mechanical coupling between the nucleus, cytoskeleton and the ECM. The cell is modeled as an active spherical inclusion, containing a round nucleus at its center, and embedded in a 3D elastic matrix. We investigate three sources of cellular stress: spreading-induced stress, actomyosin contractility and chromatin entropic forces. Formulating the coupling of actomyosin contractility to the local stress we predict the consequences that the nucleus, cytoskeleton and ECM mechanical properties may have on the overall force-balance in the cell and the perinuclear acto-myosin polarization. We demonstrate that the presence of the nucleus induces symmetry breaking of the elastic stress that, we predict, elastically tends to orient actomyosin alignment tangentially around the nucleus; the softer the nucleus or the matrix, the stronger is the preference for tangential alignment. Spreading induced stresses may induce radial actomyosin alignment near stiff nuclei. In addition, we show that in regions of high actomyosin density myosin motors have an elastic tendency to orient tangentially as often occurs near the cell periphery. These conclusions highlight the role of the nucleus in the regulation of cytoskeleton organization and may provide new insight into the mechanics of stem cell differentiation involving few fold increase in nucleus stiffness.