Nonlinear elasticity and rheological response in epithelial tissues

In the process of embryonic development, tissues experience significant reshaping to create functional organs. Adult animals also face ongoing mechanical stresses and deformations in their cells and tissues to maintain physiological functions. The ability of cells to resist these mechanical forces, as well as to flow collectively, is crucial for both embryonic development and adult physiology. These mechanical changes can be self-generated at the cellular level or imposed externally by adjacent tissues and organs. Past research in tissue mechanics has often focused either on how tissues respond to external forces or on the internal stresses generated within the cells. In contrast, our study integrates both aspects using a 2D active vertex model of confluent tissue. We investigate how external forces applied across the tissue interact with internal stresses arising from cellular movements.

Specifically, we explore how the balance between external and internal forces influences the overall mechanical behavior of the tissue. Our focus is on tissues that are near a transition point between behaving like a solid or a fluid, known as the jamming/unjamming transition. In such tissues, we identify a range of intriguing rheological properties, including yielding, shear thinning, continuous shear thickening (CST), and discontinuous shear thickening (DST). Our model offers a comprehensive framework for understanding the complex, nonlinear rheological behaviors observed in living tissues.