Unified theoretical framework for epithelial mechanics, rheology and 3D shaping by upscaling active gels models of the actin cortex

Recent observations across various species have revealed a rich phenomenology of epithelial mechanics arising from the active-viscoelasticity and turnover of the actomyosin cortex. However, a link between the subcellular cortical dynamics and the tissue scale response has been lacking in theoretical models of epithelia. We address this gap by developing a formalism which bridges the active-gel models of the cortex and vertex-like models at a tissue scale. We show that this modeling approach provides a unified framework capturing numerous seemingly disconnected epithelial phenomenologies such as stress relaxation following step-strain maneuvers (Casares et al, Nat. Mat., 2015; Khalilgharibi et al, Nat. Phys., 2019), solid-like or fluid-like creep behavior (Harris et al, PNAS, 2012), buckling and transient buckling upon compression (Wyatt et al, Nat. Mat., 2020), pulsatile contractions during Drosophila dorsal closure (Solon et al, Cell, 2009), spontaneous curling (Fouchard et al, PNAS, 2020) and active superelasticity (Latorre et al, Nature, 2018). Overall, the proposed framework provides a systematic procedure to examine the effect at the epithelial scale of sub-cellular cortical dynamics and, in the process, ties a diverse epithelial phenomenology to a common subcellular origin.