Fig. 4: 2D tissue dynamics and the active cohesion hypothesis.
a Sequential snapshots from a dynamic simulation of a 2D cellular sheet with EIC in an oscillatory mode (Supplementary Movie 3 left). Shown, is a case of area-trigger (where a cell’s critical area ac is lower than its rest-area a0). Similar patterns appear with a perimeter-trigger (where a critical perimeter, pc, is lower than the rest-perimeter p0). Greyscale represents cell area; red dots represent actively contracting cells. The white arrows highlight the propagation of circular and spiral pulses that have features similar to the 1D case: an extension front, followed by a shrinking front, while all cells in between are actively contracting. b Adding a yielding response to the model: when the tension on a cell–cell junction is higher than a critical value, σs, an immediate softening occurs in both neighboring cells: a reduction in stiffness from k to ks (In the 2D case, the softening can be either in the perimeter stiffness kp or area stiffness ka). In the sketch, arrows mark contractions, dashed blue lines mark softening. c Snapshots from a simulation of a tissue with both contraction and softening thresholds (Supplementary Movie 3 right). Red dots mark contracting cells, blue hexagons mark softened cells. The white arrows highlight the propagation of pulses with softening fronts accompanying the extension and shrinkage fronts. d–g Testing the response of an excitable tissue (pc > p0) to external stretch in the x-axis: d The pulling configuration: A constant force is pulling uniaxially on the sheet, acting directly on a fixed set of cells on each side (marked with red dashed circles). e The distance between the pulling points L, normalized to the distance at rest L0, as a function of time. f We present peak values of mechanical fields per pixel across the tissue. We show the maximal cell perimeter strain (p/p0), area strain (a/a0) and junction stress (σ) throughout the simulation. We compare a passive material, a material with contraction response (EIC) and a material with both EIC and yielding responses. The contractile material dynamically distributes the strains in the tissue but presents high levels of junction stress. A material with the added yield-response increases slightly the levels of cell strain but cuts-off high junction stress values. See also Supplementary Movie 4 and Supplementary Fig. 3. g Histogram-view of all data points in the pulling simulation.
