Mapping mechanical stress in curved epithelia of designed size and shape.

The function of organs such as lungs, kidneys and mammary glands relies on the three-dimensional geometry of their epithelium. To adopt shapes such as spheres, tubes and ellipsoids, epithelia generate mechanical stresses that are generally unknown. Here we engineer curved epithelial monolayers of controlled size and shape and map their state of stress. We design pressurized epithelia with circular, rectangular and ellipsoidal footprints. We develop a computational method, called curved monolayer stress microscopy, to map the stress tensor in these epithelia. This method establishes a correspondence between epithelial shape and mechanical stress without assumptions of material properties. In epithelia with spherical geometry we show that stress weakly increases with areal strain in a size-independent manner. In epithelia with rectangular and ellipsoidal cross-section we find pronounced stress anisotropies that impact cell alignment. Our approach enables a systematic study of how geometry and stress influence epithelial fate and function in three-dimensions.

Mechanical compartmentalization of the intestinal organoid enables crypt folding and collective cell migration.

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 at present 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 extracellular matrix and folds through apical constriction, whereas the transit amplifying zone pulls the extracellular matrix and elongates through basal constriction. The size of the stem cell compartment depends on the extracellular-matrix stiffness and endogenous cellular forces. Computational modelling 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.

The 2020 motile active matter roadmap.

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. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Active superelasticity in three-dimensional epithelia of controlled shape.

Fundamental biological processes are carried out by curved epithelial sheets that enclose a pressurized lumen. How these sheets develop and withstand three-dimensional deformations has remained unclear. Here we combine measurements of epithelial tension and shape with theoretical modelling to 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 strains in the tissue are accommodated by highly heterogeneous strains at a cellular level, in seeming contradiction to the measured tensional uniformity. This phenomenon is reminiscent of superelasticity, a behaviour that is generally attributed to microscopic material instabilities in metal alloys. We show that in epithelial cells this instability is triggered by a stretch-induced dilution of the actin cortex, and is rescued by the intermediate filament network. Our study reveals a type of mechanical behaviour-which we term active superelasticity-that enables epithelial sheets to sustain extreme stretching under constant tension.

Morphological study of elastic-plastic-brittle transitions in disordered media.

We use a spring lattice model with springs following a bilinear elastoplastic-brittle constitutive behavior with spatial disorder in the yield and failure thresholds to study patterns of plasticity and damage evolution. The elastic-perfectly plastic transition is observed to follow percolation scaling with the correlation length critical exponent ν≈1.59, implying the universality class corresponding to the long-range correlated percolation. A quantitative analysis of the plastic strain accumulation reveals a dipolar anisotropy (for antiplane loading) which vanishes with increasing hardening modulus. A parametric study with hardening modulus and ductility controlled through the spring level constitutive response demonstrates a wide spectrum of behaviors with varying degree of coupling between plasticity and damage evolution.

Elastic-plastic-brittle transitions and avalanches in disordered media.

A spring lattice model with the ability to simulate elastic-plastic-brittle transitions in a disordered medium is presented. The model is based on bilinear constitutive law defined at the spring level and power-law-type disorder introduced in the yield and failure limits of the springs. The key parameters of the proposed model effectively control the disorder distribution, significantly affecting the stress-strain response, the damage accumulation process, and the fracture surfaces. The model demonstrates a plastic strain avalanche behavior for perfectly plastic as well as hardening materials with a power-law distribution, in agreement with the experiments and related models. The strength of the model is in its generality and ability to interpolate between elastic-plastic hardening and elastic-brittle transitions.