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.

From coffee beans flowing in a chute to cells remodelling in a living tissue, a wide variety of close-packed collective systems— both inert and living—have the potential to jam. The collective can sometimes flow like a fluid or jam and rigidify like a solid. The unjammed-to-jammed transition remains poorly understood, however, and structural properties characterizing these phases remain unknown. Using primary human bronchial epithelial cells, we show that the jamming transition in asthma is linked to cell shape, thus establishing in that system a structural criterion for cell jamming. Surprisingly, the collapse of critical scaling predicts a counter-intuitive relationship between jamming, cell shape and cell–cell adhesive stresses that is borne out by direct experimental observations. Cell shape thus provides a rigorous structural signature for classification and investigation of bronchial epithelial layer jamming in asthma, and potentially in any process in disease or development in which epithelial dynamics play a prominent role.

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...

Endothelial cell alignment along the direction of laminar fluid flow is widely understood to be a defining morphological feature of vascular homeostasis. While the role of associated signaling and structural events have been well studied, associated intercellular stresses under laminar fluid shear have remained ill-defined and the role of these stresses in the alignment process has remained obscure. To fill this gap, we report here the tractions as well as the complete in-plane intercellular stress fields measured within the human umbilical vein endothelial cell (HUVEC) monolayer subjected to a steady laminar fluid shear of 1 Pa. Tractions, intercellular stresses, as well as their time course, heterogeneity, and anisotropy, were measured using monolayer traction microscopy and monolayer stress microscopy. Prior to application of laminar fluid flow, intercellular stresses were largely tensile but fluctuated dramatically in space and in time (317 ± 122 Pa). Within 12 h of the onset of laminar fluid flow, the intercellular stresses decreased substantially but continued to fluctuate dramatically (142 ± 84 Pa). Moreover, tractions and intercellular stresses aligned strongly and promptly (within 1 h) along the direction of fluid flow, whereas the endothelial cell body aligned less strongly and substantially more slowly (12 h). Taken together, these results reveal that steady laminar fluid flow induces prompt reduction in magnitude and alignment of tractions and intercellular stress tensor components followed by the retarded elongation and alignment of the endothelial cell body. Appreciably smaller intercellular stresses supported by cell-cell junctions logically favor smaller incidence of gap formation and thus improved barrier integrity.

Protein structure prediction is beginning to be, at least partially, successful. Evaluating predictions, however, has many elements of subjectivity, making it difficult to determine the nature and extent of improvements that are most needed. We describe how the funnel-like nature of energy functions used for protein structure prediction determines their quality and can be quantified using landscape theory and multiple histogram sampling methods. Prediction algorithms exhibit a "caldera"-like landscape rather than a perfectly funneled one. Estimates are made of the expected number of effectively distinct structures produced by a prediction algorithm.