Equilibrium mechanics of monolayered epithelium

In order to fully understand the epithelial mechanics it is essential to integrate different levels of epithelial organization. In this work, we propose a theoretical approach for connecting the macroscopic mechanical properties of a monolayered epithelium to the mechanical properties at the cellular level. The analysis is based on the established mechanical models-at the macroscopic scale the epithelium is described within the mechanics of thin layers, while the cellular level is modeled in terms of the cellular surface (cortical) tension and the intercellular adhesion. The macroscopic elastic energy of the epithelium is linked to the energy of an average epithelial cell. The epithelial equilibrium state is determined by energy minimization and the macroscopic elastic moduli are calculated from deformations around the equilibrium. The results indicate that the epithelial equilibrium state is defined by the ratio between the adhesion strength and the cellular surface tension. The lower and the upper bounds for this ratio are estimated. If the ratio is small, the epithelium is cuboidal, if it is large, the epithelium becomes columnar. Importantly, it is found that the cellular cortical tension and the intercellular adhesion alone cannot produce the flattened squamous epithelium. Any difference in the surface tension between the apical and basal cellular sides bends the epithelium towards the side with the larger surface tension. Interestingly, the analysis shows that the epithelial area expansivity modulus and the shear modulus depend only on the cellular surface tension and not on the intercellular adhesion. The results are presented in a general analytical form, and are thus applicable to a variety of monolayered epithelia, without relying on the specifics of numerical finite-element methods. In addition, by using the standard theoretical tools for multi-laminar systems, the results can be applied to epithelia consisting of layers with different mechanical properties.