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Adhering cells exert traction forces on the underlying substrate. We numerically investigate the intimate relation between traction forces, the structure of the actin cytoskeleton, and the shape of cells adhering to adhesive micropatterned substrates. By combining the Cellular Potts Model with a model of cytoskeletal contractility, we reproduce prominent anisotropic features in previously published experimental data on fibroblasts, endothelial cells, and epithelial cells on adhesive micropatterned substrates. Our work highlights the role of cytoskeletal anisotropy in the generation of cellular traction forces, and provides a computational strategy for investigating stress fiber anisotropy in dynamical and multicellular settings.Author summaryCells that make up multicellular life perform a variety of mechanical tasks such as pulling on surrounding tissue to close a wound. The mechanisms by which cells perform these tasks are, however, incompletely understood. In order to better understand how they generate forces on their environment, cells are often studied in vitro on compliant substrates, which deform under the so called “traction forces” exerted by the cells. Mathematical models complement these experimental approaches because they help to interpret the experimental data, but most models for traction forces on adhesive substrates assume that cells contract isotropically, i.e., they do not contract in a specific direction. However, many cell types contain organized structures of stress fibers - strong contracting cables inside the cell - that enable cells to exert forces on their environment in specific directions only. Here we present a computational model that predicts both the orientations of these stress fibers as well as the forces that cells exert on the substrates. Our model reproduces both the orientations and magnitudes of previously reported experimental traction forces, and could serve as a starting point for exploring mechanical interactions in multicellular settings.

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.

Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monolayers and investigate how chirality affects the motion of topological defects, as well as the collective motion in stripe-shaped domains. We find that chirality introduces a characteristic asymmetry in the collective cellular flow, from which the ratio between chiral and non-chiral active stresses can be inferred by particle-image-velocimetry measurements. Furthermore, we find that chirality changes the nature of the spontaneous flow transition under confinement and that, for specific anchoring conditions, the latter has the structure of an imperfect pitchfork bifurcation., Comment: 12 pages, 5 figures. Version accepted for publication in Soft Matter

Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as topotaxis, is especially prominent among cells persistently crawling within a spatially varying distribution of cell-sized obstacles. In this article we introduce a toy model of topotaxis based on active Brownian particles constrained to move in a lattice of obstacles, with space-dependent lattice spacing. Using numerical simulations and analytical arguments, we demonstrate that topographical gradients introduce a spatial modulation of the particles' persistence, leading to directed motion toward regions of higher persistence. Our results demonstrate that persistent motion alone is sufficient to drive topotaxis and could serve as a starting point for more detailed studies on self-propelled particles and cells., Comment: 10 pages, 6 figures

We investigate the geometrical and mechanical properties of adherent cells characterized by a highly anisotropic actin cytoskeleton. Using a combination of theoretical work and experiments on micropillar arrays, we demonstrate that the shape of the cell edge is accurately described by elliptical arcs, whose eccentricity expresses the degree of anisotropy of the internal cell stresses. This results in a spatially varying tension along the cell edge, that significantly affects the traction forces exerted by the cell on the substrate. Our work highlights the strong interplay between cell mechanics and geometry and paves the way towards the reconstruction of cellular forces from geometrical data., 5 pages, 3 figures

The shape of a cell membrane is largely defined by the underlying actin cytoskeleton and membrane mechanics. The actin cytoskeleton asserts contractile forces on the membrane that can be divided in isotropic and directed forces. We present a theory which is an extension of the Young-Laplace equation. It models cell edges as parts of one uniform ellipse, which changes from cell to cell. The ellipse parameters are characterized by the ratio of isotropic to directed contractility of the cell. We demonstrate the capabilities of this model using fibroblasts seeded on an elastic micro-pillar array. In this way adhesion forces exerted by the cell at single adhesion sites are measured. We show that isotropic and directed forces balance the line tension in cortical actin. Furthermore, for cells with homogeneous contractile forces and a single orientation of stress-fibers any part of the cell edge follows a universal ellipse, enabling us to calculate the magnitude of isotropic and directed contractility in a single cell. We show that in 3T3 fibroblasts the directed contractility is about three times as strong as the isotropic contractility. If myosin motors are inhibited, however, directed contractility decreases, effectively disabling forces generated by stress-fibers, and the elliptical cell cortex turns into a circular shape predicted for an isotropic contractile cytoskeleton. Our analysis shows that a simple two-parameter model explains polarity, shape of the cell cortex and cellular forces as experimentally observed. Potentially this model can be used to predict stresses and forces on the extracellular matrix and tissue.