The ability of cells to follow gradients of extracellular matrix stiffness—durotaxis—has been implicated in development, fibrosis, and cancer. Here, we found multicellular clusters that 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, required the action of myosin motors, and originated from supracellular transmission of contractile physical forces. To explain the observed phenomenology, we developed a generalized clutch model in which local stick-slip dynamics of cell-matrix adhesions was 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.

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 α_vβ₆ 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.

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.

The Heisenberg nearest-neighbor antiferromagnet on the pyrochlore (three-dimensional) lattice is highly frustrated and does not order at low temperature where spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions (DMI’s) 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’s (if present) tremendously change the low-temperature behavior of the system. At a temperature of the order of the DMI’s a phase transition to a long-range-ordered state takes place. The ordered magnetic structures are explicited for the different possible DMI’s 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 discussed.