Cheikh, M. I. | Search bioRxiv

bioRxiv2023

A 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.

biophysics↗

bioRxiv2022

Cantilever-based in vivo measurements in the early Drosophila embryo reveal adiabatic elastic response on developmentally relevant time scales

In order to understand morphogenesis, it is necessary to know the material properties or forces shaping the living tissue. In spite of this need, very few in vivo measurements are currently available. Here, using the early Drosophila embryo as a model, we describe a novel cantilever-based technique which allows for the simultaneous quantification of applied force and tissue displacement in a living embryo. By analyzing data from a series of experiments in which embryonic epithelium is subjected to developmentally relevant perturbations, we conclude that the response to applied force is adiabatic and is dominated by elastic forces and geometric constraints, or system size effects. Crucially, computational modeling of the experimental data indicated that the apical surface of the epithelium must be softer than the basal surface, a result which we confirmed experimentally. Further, we used the combination of experimental data and comprehensive computational model to estimate the elastic modulus of the apical surface and set a lower bound on the elastic modulus of the basal surface. More generally, our investigations revealed important general features that we believe should be more widely addressed when quantitatively modeling tissue mechanics in any system. Specifically, different compartments of the same cell can have very different mechanical properties; when they do, they can contribute differently to different mechanical stimuli and cannot be merely averaged together. Additionally, tissue geometry can play a substantial role in mechanical response, and cannot be neglected.

biophysics↗