Inferring the flow properties of epithelial tissues from their geometry. (10th March 2021)

• Record Type: Journal Article
• Authors: Popović, Marko; Druelle, Valentin; Dye, Natalie A; Jülicher, Frank; Wyart, Matthieu
• Is Part Of: New journal of physics. Volume 23:Number 3(2021)
• Publication Date: 2021-03-10
• Subjects: tissue mechanics -- vertex model -- plasticity -- T1 transition; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/abcbc7
• Languages: English
• ISSNs: 1367-2630

Abstract

Abstract: Amorphous materials exhibit complex material properties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while they start to yield above a critical stress Σc . A key quantity controlling plasticity which is, however, hard to measure is the density P ( x ) of weak spots, where x is the additional stress required for local plastic failure. In the thermodynamic limit P ( x ) ∼ x θ is singular at x = 0 in the solid phase below the yield stress Σc . This singularity is related to the presence of system spanning avalanches of plastic events. Here we address the question if the density of weak spots and the flow properties of a material can be determined from the geometry of an amorphous structure alone. We show that a vertex model for cell packings in tissues exhibits the phenomenology of plastic amorphous systems. As the yield stress is approached from above, the strain rate vanishes and the avalanches size S and their duration τ diverge. We then show that in general, in materials where the energy functional depends on topology, the value x is proportional to the length L of a bond that vanishes in a plastic event. For this class of models P ( x ) is therefore readily measurable from geometry alone. Applying this approach to a quantification of the cell packing geometry in the developing wing epithelium of the fruit fly, we find that in this tissue P ( L ) exhibits a power law with exponents similar to those found numerically for a vertex model in its solid phase. This suggests that this tissue exhibits plasticity and non-linear material properties that emerge from collective cell behaviors and that these material properties govern developmental processes. Our approach based on the relation between topology and energetics suggests a new route to outstanding questions associated with the yielding transition.