Abstract:The ability of cells to follow gradients of extracellular matrix stiffnessdurotaxis-has been implicated in development, fibrosis and cancer. Durotaxis is established as a single cell phenomenon but whether it can direct the motion of cell collectives is unknown. Here we found that multicellular clusters exhibited durotaxis even if isolated constituent cells did not. This emergent mode of directed collective cell migration applied to a variety of epithelial cell types, and required the action of myosin motors and the integrity of cell-cell junctions. By extending traction microscopy to extracellular matrices of arbitrary stiffness profiles we showed that collective durotaxis originated from supracellular transmission of contractile physical forces. To explain the observed phenomenology, we developed a generalized clutch model in which local stickslip dynamics of cell-matrix adhesions is integrated to the tissue level through cell-cell junctions. Collective durotaxis is far more efficient than single cell durotaxis; it thus emerges as a robust mechanism to direct cell migration during development, wound healing, and collective cancer cell invasion. One Sentence Summary: Mechanical cooperation between cells enables an emergent mode of collective movement -3- Main Text:The ability of living cells to migrate following environmental gradients underlies a broad range of phenomena in development, homeostasis, and disease (1, 2). The best understood mode of directed cell migration is chemotaxis, the well-established ability of cells to follow gradients of soluble chemical cues (1). Some cell types are also able to follow gradients in the stiffness of their extracellular matrix (ECM), a process known as durotaxis (3-10).Durotaxis has been implicated in development (11), fibrosis (12) and cancer (13), but its underlying mechanisms remain unclear.Most of our understanding of directed cell migration has been obtained in single isolated cells. However, fundamental processes during development, wound healing, tissue regeneration, and some forms of cancer cell invasion are driven by directed migration of cell groups (14-16). Cell-cell interactions within these groups provide cooperative mechanisms of cell guidance that are altogether inaccessible to single cells (14-20). Here we investigated whether cell groups undergo collective durotaxis, and the cooperative nature of underlying mechanisms.Using stencils of magnetic PDMS, we micropatterned rectangular clusters (500 µm width) of human mammary epithelial cells (MCF-10A) on fibronectin-coated polyacrylamide gel substrates exhibiting uniform stiffness or a stiffness gradient (51 ± 17 kPa/mm, Fig. S1) (21). Upon removal of the PDMS stencil, clusters migrating on uniform gels displayed symmetric expansion (Fig. 1A,C,E,G, Fig. S2, Movie S1), whereas clusters migrating on stiffness gradients displayed a robust asymmetry characterized by faster, more persistent expansion towards the stiff edge (Fig. 1B-D-F-H, Fig. S2, Movie S1). This result was also -4-observed in clusters of...

Tissue rigidity regulates processes in development, cancer and wound healing. However, how cells detect rigidity, and thereby modulate their behaviour, remains unknown. Here, we show that sensing and adaptation to matrix rigidity in breast myoepithelial cells is determined by the bond dynamics of different integrin types. Cell binding to fibronectin through either α5β1 integrins (constitutively expressed) or αvβ6 integrins (selectively expressed in cancer and development) adapts force generation, actin flow, and integrin recruitment to rigidities associated with healthy or malignant tissue, respectively. In vitro experiments and theoretical modelling further demonstrate that this behaviour is explained by the different binding and unbinding rates of both integrin types to fibronectin. Moreover, rigidity sensing through differences in integrin bond dynamics applies both when integrins bind separately and when they compete for binding to fibronectin.

The Heisenberg nearest neighbour antiferromagnet on the pyrochlore (3D) lattice is highly frustrated and does not order at low temperature where spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions (DMI) may be present in pyrochlore compounds as is shown, and the consequences of such interactions on the magnetic properties are investigated through mean field approximation and monte carlo simulations. It is found that DMI (if present) tremendously change the low temperature behaviour of the system. At a temperature of the order of the DMI a phase transition to a long range ordered state takes place. The ordered magnetic structures are explicited for the different possible DMI which are introduced on the basis of symmetry arguments. The relevance of such a scenario for pyrochlore compounds in which an ordered magnetic structure is observed experimentally is dicussed.

Shape-dependent local differentials in cell proliferation are considered to be a major driving mechanism of structuring processes in vivo, such as embryogenesis, wound healing, and angiogenesis. However, the specific biophysical signaling by which changes in cell shape contribute to cell cycle regulation remains poorly understood. Here, we describe our study of the roles of nuclear volume and cytoskeletal mechanics in mediating shape control of proliferation in single endothelial cells. Micropatterned adhesive islands were used to independently control cell spreading and elongation. We show that, irrespective of elongation, nuclear volume and apparent chromatin decondensation of cells in G1 systematically increased with cell spreading and highly correlated with DNA synthesis (percent of cells in the S phase). In contrast, cell elongation dramatically affected the organization of the actin cytoskeleton, markedly reduced both cytoskeletal stiffness (measured dorsally with atomic force microscopy) and contractility (measured ventrally with traction microscopy), and increased mechanical anisotropy, without affecting either DNA synthesis or nuclear volume. Our results reveal that the nuclear volume in G1 is predictive of the proliferative status of single endothelial cells within a population, whereas cell stiffness and contractility are not. These findings show that the effects of cell mechanics in shape control of proliferation are far more complex than a linear or straightforward relationship. Our data are consistent with a mechanism by which spreading of cells in G1 partially enhances proliferation by inducing nuclear swelling and decreasing chromatin condensation, thereby rendering DNA more accessible to the replication machinery.

Many fundamental cell processes, such as angiogenesis, neurogenesis and cancer metastasis, are thought to be modulated by extracellular matrix stiffness. Thus, the availability of matrix substrates having well-defined stiffness profiles can be of great importance in biophysical studies of cell-substrate interaction. Here, we present a method to fabricate biocompatible hydrogels with a well defined and linear stiffness gradient. This method, involving the photopolymerization of films by progressively uncovering an acrylamide/bis-acrylamide solution initially covered with an opaque mask, can be easily implemented with common lab equipment. It produces linear stiffness gradients of at least 115 kPa/mm, extending from ∼1 kPa to 240 kPa (in units of Young's modulus). Hydrogels with less steep gradients and narrower stiffness ranges can easily be produced. The hydrogels can be covalently functionalized with uniform coatings of proteins that promote cell adhesion. Cell spreading on these hydrogels linearly correlates with hydrogel stiffness, indicating that this technique effectively modifies the mechanical environment of living cells. This technique provides a simple approach that produces steeper gradients, wider rigidity ranges, and more accurate profiles than current methods.

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The rheology of neutrophils in their passive and activated states plays a key role in determining their function in response to inflammatory stimuli. Atomic force microscopy was used to study neutrophil rheology by measuring the complex shear modulus G*(omega) of passive nonadhered rat neutrophils on poly(HEMA) and neutrophils activated through adhesion to glass. G*(omega) was measured over three frequency decades (0.1-102.4 Hz) by indenting the cells 500 nm with a spherical tip and then applying a 50-nm amplitude multi-frequency signal. G*(omega) of both passive and adhered neutrophils increased as a power law with frequency, with a coupling between elastic (G') and loss (G'') moduli. For passive neutrophils at 1.6 Hz, G' = 380 +/- 121 Pa, whereas G'' was fourfold smaller and the power law coefficient was of x = 1.184. Adhered neutrophils were over twofold stiffer with a lower slope (x = 1.148). This behavior was adequately described by the power law structural damping model but not by liquid droplet and Kelvin models. The increase in stiffness with frequency may modulate neutrophil transit, arrest, and transmigration in vascular microcirculation.

For an organism to develop and maintain homeostasis, cell types with distinct functions must often be separated by physical boundaries. The formation and maintenance of such boundaries are commonly attributed to local mechanisms restricted to the cells lining the boundary. Here we show that, besides these local subcellular mechanisms, the formation and maintenance of tissue boundaries involves long-lived, long-ranged mechanical events. We analyzed the formation of repulsive epithelial boundaries between two epithelial monolayers, one expressing the receptor tyrosine kinase EphB2 and one expressing its ligand ephrinB1. Upon contact, both monolayers exhibited oscillatory patterns of traction forces and intercellular stresses that spanned several cell rows and tended to pull cell-matrix adhesions away from the boundary. With time, monolayers jammed and supracellular force patterns became long-lived, thereby permanently sustaining tissue segregation. Jamming was paralleled by the emergence of deformation waves that propagated away from the boundary. This phenomenon was not specific to EphB2/ephrinB1 repulsion but was also present during the formation of boundaries with an inert interface and during fusion of homotypic epithelial layers. Our findings thus unveil a global physical mechanism that sustains tissue separation independently of the biochemical and mechanical features of the local tissue boundary.