A scaling law for epithelial tissue rheology

Abstract

Predictive mechanistic understanding of morphogenesis absolutely requires quantitative knowledge of the mechanical properties of embryonic tissues. Our lab has recently established a set of experimental tools that have allowed us to directly probe tissue material properties in the living early embryo of Drosophila melanogaster. Here, we develop a simple quantitative theory explaining our central experimental observation: when subjected to concentrated constant pulling force, epithelium deforms following a power law with an exponent of 1/2. Our analysis explains this finding in terms of two physical effects: (1) actin turnover and (2) geometric nonlinearity due to the floppy topology of the cellular network, and has additionally allowed us to measure the effective spring constant of a cellular edge.