Feedback-controlled mechanics of tissue vertex model: emergent soft elasticity and active yielding

Abstract

Biological tissues exhibit diverse mechanical and rheological behaviors during morphogenesis. While much is known about tissue phase transitions controlled by structural order and cell mechanics, key questions regarding how tissue-scale nematic order emerges from cell-scale processes and influences tissue rheology remain unclear. Here, we develop a minimal vertex model that incorporates a coupling between active forces generated by cytoskeletal fibers and their alignment with local elastic stress in solid epithelial tissues. Combining theory and simulations, we show that this feedback loop induces an isotropic--nematic transition, leading to an ordered solid state that exhibits soft elasticity. Further increasing activity drives collective self-yielding, that is the ability to spontaneously transition form elastic to plastic deformations, with tissue flows that are correlated across the entire system. We argue that this remarkable state, that we dub plastic nematic solid, is uniquely suited to facilitate active tissue remodeling during morphogenesis. It fundamentally differs from the well-studied fluid regime where macroscopic elastic stresses vanish and the velocity correlations remain short-ranged. Altogether, our theoretical results reveal a rich spectrum of tissue states jointly governed by activity and passive cell deformability, with important implications for understanding tissue mechanics and morphogenesis.