Scaling Law for Epithelial Tissue Rheology

Epithelial morphogenesis is a process through which simple cellular sheets are shaped into complex tissues and organs in a developing animal. From a physics perspective, understanding any shape change requires knowing the active forces driving its dynamics, as well as the material properties, i.e., the rheology, of the material that is undergoing the deformation. Despite a long-standing effort, rheological properties of embryonic tissues have remained elusive. Here, we develop a minimal theory providing a comprehensive explanation of rheological measurements characterizing the mechanics of epithelia in the early fly embryo. Our theory explains a key experimental observation: when subjected to concentrated pulling force, the embryonic epithelium of the fruit fly Drosophila melanogaster deforms following a power law with an exponent of 1/2. All dimensional parameters of our theory are constrained by direct measurements and have allowed us to estimate the spring constant of an individual cellular edge. We show that stress relaxation (attributable to actin turnover), stretching elasticity of individual cellular edges, and the floppy topology of the cellular network are the sole physical properties governing tissue rheology on the developmentally relevant time scale of 1-10 minutes.