Abstract
Epithelial tissues are sheet-like tissue structures that line the inner and outer surfaces of animal bodies and organs. Their remarkable ability to actively produce, or passively adapt to, complex surface geometries has fascinated physicists and biologists alike for centuries. The most simple and yet versatile process of epithelial deformation is epithelial folding, through which curved shapes, tissue convolutions and internal structures are produced. The advent of quantitative live imaging, combined with experimental manipulation and computational modeling, has rapidly advanced our understanding of epithelial folding. In particular, a set of mechanical principles has emerged to illustrate how forces are generated and dissipated to instigate curvature transitions in a variety of developmental contexts. Folding a tissue requires that mechanical loads or geometric changes be non-uniform. Given that polarity is the most distinct and fundamental feature of epithelia, understanding epithelial folding mechanics hinges crucially on how forces become polarized and how polarized differential deformation arises, for which I coin the term 'mechanical polarity'. In this review, five typical modules of mechanical processes are distilled from a diverse array of epithelial folding events. Their mechanical underpinnings with regard to how forces and polarity intersect are analyzed to accentuate the importance of mechanical polarity in the understanding of epithelial folding.
