A tension-based model of flat and corrugated simple epithelia

Abstract

We theoretically study the shape of single-cell-thick epithelium consisting of incompressible fluid cells. The cells carry a surface energy associated with cortex and interfacial tension as well as cell–cell adhesion such that the basal, the lateral, and the apical cell faces are each characterized by a specific effective surface tension. In our reduced-dimensionality version of the model, the epithelium consists of a linear chain of quadrilateral cells. We explore the 1D periodic minimal-energy configurations of the tissue, finding that they include both flat and corrugated states. As the differential apical-basal tension is increased, the epithelium undergoes a transition from the thin flat state to the expanded corrugated state which is then compactified and transformed into the collapsed corrugated state and eventually replaced by the thick flat state. Apart from the restriction to the globally uncurved space, the corrugated states are shaped by apical constriction and cell impenetrability. We also analyze the elastic properties of these states, focusing on the stretching modulus and the torque exerted on the substrate.