Cells comprising a tissue migrate as part of a collective. How collective processes are coordinated over large multi-cellular assemblies has remained unclear, however, because mechanical stresses exerted at cell-cell junctions have not been accessible experimentally. We report here maps of these stresses within and between cells comprising a monolayer. Within the cell sheet there arise unanticipated fluctuations of mechanical stress that are severe, emerge spontaneously, and ripple across the monolayer. This stress landscape becomes increasingly rugged, sluggish, and cooperative with increasing system density. Within that landscape, local cellular migrations follow local orientations of maximal principal stress. Migrations of both endothelial and epithelial monolayers conform to this behavior, as do breast cancer cell lines before but not after the epithelial-mesenchymal transition. Collective migration in these diverse systems is seen to be governed by a simple but unifying physiological principle: neighboring cells join forces to transmit appreciable normal stress across the cell-cell junction, but migrate along orientations of minimal intercellular shear stress.

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Cells alter their mechanical properties in response to their local microenvironment; this plays a role in determining cell function and can even influence stem cell fate. Here, we identify a robust and unified relationship between cell stiffness and cell volume. As a cell spreads on a substrate, its volume decreases, while its stiffness concomitantly increases. We find that both cortical and cytoplasmic cell stiffness scale with volume for numerous perturbations, including varying substrate stiffness, cell spread area, and external osmotic pressure. The reduction of cell volume is a result of water efflux, which leads to a corresponding increase in intracellular molecular crowding. Furthermore, we find that changes in cell volume, and hence stiffness, alter stem-cell differentiation, regardless of the method by which these are induced. These observations reveal a surprising, previously unidentified relationship between cell stiffness and cell volume that strongly influences cell biology.cell volume | cell mechanics | molecular crowding | gene expression | stem cell fate C ell volume is a highly regulated property that affects myriad functions (1, 2). It changes over the course of the cell life cycle, increasing as the cell plasma membrane grows and the amount of protein, DNA, and other intracellular material increases (3). However, it can also change on a much more rapid time scale, as, for example, on cell migration through confined spaces (4, 5); in this case, the volume change is a result of water transport out of the cell. This causes increased concentration of intracellular material and molecular crowding, having numerous important consequences (6, 7). Alternately, the volume of a cell can be directly changed through application of an external osmotic pressure. This forces water out of the cell, which also decreases cell volume, increases the concentration of intracellular material, and intensifies molecular crowding. Application of an external osmotic pressure to reduce cell volume also has other pronounced manifestations: For example, it leads to a significant change in cell mechanics, resulting in an increase in stiffness (8); it also impacts folding and transport of proteins (9), as well as condensation of chromatin (10). These dramatic effects of osmotic-induced volume change on cell behavior raise the question of whether cells ever change their volume through water efflux under isotonic conditions, perhaps to modulate their mechanics and behavior through changes in molecular crowding.Here, we demonstrate that when cells are cultured under the same isotonic conditions, but under stiffer extracellular environments, they reduce their cell volume through water efflux out of the cell, and this has a large and significant impact on cell mechanics and cell physiology. Specifically, as a cell spreads out on a stiff substrate, its volume decreases, and the cell behaves in a similar manner to that observed for cells under external osmotic pressure: Both the cortical and cytoplasmic stiffness increase as the vol...

Mechanical robustness of the cell under different modes of stress and deformation is essential to its survival and function. Under tension, mechanical rigidity is provided by the cytoskeletal network; with increasing stress, this network stiffens, providing increased resistance to deformation. However, a cell must also resist compression, which will inevitably occur whenever cell volume is decreased during such biologically important processes as anhydrobiosis and apoptosis. Under compression, individual filaments can buckle, thereby reducing the stiffness and weakening the cytoskeletal network. However, the intracellular space is crowded with macromolecules and organelles that can resist compression. A simple picture describing their behavior is that of colloidal particles; colloids exhibit a sharp increase in viscosity with increasing volume fraction, ultimately undergoing a glass transition and becoming a solid. We investigate the consequences of these 2 competing effects and show that as a cell is compressed by hyperosmotic stress it becomes progressively more rigid. Although this stiffening behavior depends somewhat on cell type, starting conditions, molecular motors, and cytoskeletal contributions, its dependence on solid volume fraction is exponential in every instance. This universal behavior suggests that compressioninduced weakening of the network is overwhelmed by crowdinginduced stiffening of the cytoplasm. We also show that compression dramatically slows intracellular relaxation processes. The increase in stiffness, combined with the slowing of relaxation processes, is reminiscent of a glass transition of colloidal suspensions, but only when comprised of deformable particles. Our work provides a means to probe the physical nature of the cytoplasm under compression, and leads to results that are universal across cell type.T he abilities of the eukaryotic cell to maintain shape, flow, and remodel are mechanical attributes of substantial biological importance (1-5), but our understanding of how cellular constituents give rise to these mechanical attributes remains incomplete. Much of the mechanical rigidity of the cell comes from the cytoskeletal network, composed primarily of actin filaments, microtubules and intermediate filaments. The cytoskeletal network is predominantly under tension; its stiffness increases with tension and thereby increases the forces it can support (6-8). However, filamentous networks typically cannot support appreciable compressive stress because filaments will lose their tension, perhaps even buckle, and thus weaken the network. Nevertheless, cellular compression occurs within tumors (9) and will always occur if the volume of the cell is decreased, as occurs in important physiological processes such as osmotic cell shrinkage, regulatory cell volume decreases (10), preservation of certain animal life forms during drought (anhydrobiosis) (11), and apoptosis (12,13).In addition to containing the cytoskeletal network, the intracellular space is filled to near capacity with macrom...

As a wound heals, or a body plan forms, or a tumor invades, observed cellular motions within the advancing cell swarm are thought to stem from yet to be observed physical stresses that act in some direct and causal mechanical fashion. Here we show that such a relationship between motion and stress is far from direct. Using monolayer stress microscopy, we probed migration velocities, cellular tractions and intercellular stresses in an epithelial cell sheet advancing towards an island on which cells cannot adhere. We found that cells located near the island exert tractions that pull systematically towards this island regardless of whether the cells approach the island, migrate tangentially along its edge or, paradoxically, recede from it. This unanticipated cell-patterning motif, which we call kenotaxis, represents the robust and systematic mechanical drive of the cellular collective to fill unfilled space.