Dynamic high-order buckling and spontaneous recovery of active epithelial tissues

Active epithelial tissues can adapt to quasi-static compressive forces through buckling instability, but their responses to dynamic forces at shorter timescales remain elusive. We firstly establish a cytoarchitectural model that can accurately capture the experimentally observed high-order buckling and postbuckling (e.g., spontaneous flattening and stress recovery) behaviors of epithelia under fast compression. It is found that the stress evolution of epithelia can be divided into three stages: loading, phase transition, and stress recovery. In the loading stage, we observe the high-order instability with a buckling mode highly correlated with the strain rate, and derive its analytical relation, showing that the rate-dependent buckling mode is quantitatively determined by the viscoelastic and geometrical characteristics of epithelia. In the phase transition and stress recovery stages, we demonstrate that the postbuckling process is governed by the active tension generated by the actomyosin network. Furthermore, by proposing a minimal model, we obtain the explicit solutions of the flattening time and stress recovery extent as functions of the applied strain or strain rate, which are in quantitative agreement with our simulations and relevant experiments. In addition, depending on the stress evolution route, we construct a universal phase diagram for the morphology evolution of the epithelia in a wide range of strain and strain rate. This study elucidates the dominative roles of the activity and rheological characteristics of active soft materials in their dynamic mechanical behaviors, offering an approach for studying the complex morphology evolution.