Role of viscoelasticity in the buckling-to-folding transition of epithelial monolayers under uni-axial compression.

Epithelial tissues often experience, and respond to, in-plane compression. This occurs during embryonic development and continues throughout adult life, driven by both internal and external forces. Gaining insight into such processes is essential for understanding the mechanisms of tissue morphogenesis, and therefore carries significant implications for developmental biology and regenerative medicine. Although the biological mechanisms associated with epithelial folding have been extensively researched, the physical mechanisms are only beginning to be clarified. One of the primary factors contributing to the relaxation of epithelial monolayers, following externally induced buckling and folding, is the viscoelasticity related to energy storage and dissipation resulting from their compression. Physical mechanisms involve the interplay between physical parameters such as: the epithelial surface tension, viscoelastic Poisson's ratio, bending modulus, internally generated strain and corresponding mechanical stress. The main focus of this review is to point out how interconnected relaxation processes influence epithelial buckling and folding as an integral part of the viscoelasticity, and how cells can regulate the extent of the folding depending on the magnitude of the externally applied compressive stress. This complex phenomenon is elaborated on substrate-devoid epithelial monolayers, considered as a simple model system under in vitro conditions.