Theory of multiscale epithelial mechanics under stretch: from active gels to vertex models

Epithelial monolayers perform a variety of mechanical functions, which include maintaining a cohesive barrier or developing 3D shapes, while undergoing stretches over a wide range of magnitudes and loading rates. To perform these functions, they rely on a hierarchical organization, which spans molecules, cytoskeletal networks, adhesion complexes and junctional networks up to the tissue scale. While the molecular understanding and ability to manipulate cytoskeletal components within cells is rapidly increasing, how these components integrate to control tissue mechanics is far less understood, partly due to the disconnect between theoretical models of sub-cellular dynamics and those at a tissue scale. To fill this gap, here we propose a formalism bridging active-gel models of the actomyosin cortex and 3D vertex-like models at a tissue scale. We show that this unified framework recapitulates a number of seemingly disconnected epithelial time-dependent phenomenologies, including stress relaxation following stretch/unstretch maneuvers, active flattening after buckling, or nonreciprocal and non-affine pulsatile contractions. We further analyze tissue dynamics probed by a novel experimental setup operating in a pressure-controlled ensemble. Overall, the proposed framework systematically connects sub-cellular cortical dynamics and tissue mechanics, and ties a variety of epithelial phenomenologies to a common sub-cellular origin.