Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of "active matter" in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano-and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics.

Fundamental biological processes are carried out by curved epithelial sheets enclosing a pressurized lumen. How these sheets develop and withstand three-dimensional deformations has remained unclear. By combining measurements of epithelial tension and shape with theoretical modeling, here we show that epithelial sheets are active superelastic materials. We produce arrays of epithelial domes with controlled geometry. Quantification of luminal pressure and epithelial tension reveals a tensional plateau over several-fold areal strains. These extreme tissue strains are accommodated by highly heterogeneous cellular strains, in seeming contradiction with the measured tensional uniformity. This phenomenology is reminiscent of superelasticity, a behavior generally attributed to microscopic material instabilities in metal alloys. We show that this instability is triggered in epithelial cells by a stretch-induced dilution of the actin cortex and rescued by the intermediate filament network. Our study unveils a new type of mechanical behavior -active superelasticity- that enables epithelial sheets to sustain extreme stretching under constant tension.

Intestinal organoids capture essential features of the intestinal epithelium such as crypt folding, cellular compartmentalization and collective movements. Each of these processes and their coordination require patterned forces that are currently unknown. Here we map three-dimensional cellular forces in mouse intestinal organoids grown on soft hydrogels. We show that these organoids exhibit a non-monotonic stress distribution that defines mechanical and functional compartments. The stem cell compartment pushes the ECM and folds through apical constriction, whereas the transit amplifying zone pulls the ECM and elongates through basal constriction. The size of the stem cell compartment depends on ECM stiffness and endogenous cellular forces. Computational modeling reveals that crypt shape and force distribution rely on cell surface tensions following cortical actomyosin density. Finally, cells are pulled out of the crypt along a gradient of increasing tension. Our study unveils how patterned forces enable compartmentalization, folding and collective migration in the intestinal epithelium.

Intestinal organoids capture essential features of the intestinal epithelium such as folding of the crypt, spatial compartmentalization of different cell types, and cellular movements from crypt to villus-like domains. Each of these processes and their coordination in time and space requires patterned physical forces that are currently unknown. Here we map the three-dimensional cell-ECM and cell-cell forces in mouse intestinal organoids grown on soft hydrogels. We show that these organoids exhibit a non-monotonic stress distribution that defines mechanical and functional compartments. The stem cell compartment pushes the ECM and folds through apical constriction, whereas the transit amplifying zone pulls the ECM and elongates through basal constriction. Tension measurements establish that the transit amplifying zone isolates mechanically the stem cell compartment and the villus-like domain. A 3D vertex model shows that the shape and force distribution of the crypt can be largely explained by cell surface tensions following the measured apical and basal actomyosin density. Finally, we show that cells are pulled out of the crypt along a gradient of increasing tension, rather than pushed by a compressive stress downstream of mitotic pressure as previously assumed. Our study unveils how patterned forces enable folding and collective migration in the intestinal crypt.