Nonlinear rheology of cellular networks

Morphogenesis depends crucially on the complex rheological properties of cell tissues and on their ability to maintain mechanical integrity while rearranging at long times. In this paper, we study the rheology of polygonal cellular networks described by a vertex model in the presence of fluctuations. We use a triangulation method to decompose shear into cell shape changes and cell rearrangements. Considering the steady-state stress under constant shear, we observe nonlinear shear-thinning behavior at all magnitudes of the fluctuations, and an even stronger nonlinear regime at lower values of the fluctuations. We successfully capture this nonlinear rheology by a mean-field model that describes the tissue in terms of cell elongation and cell rearrangements. We furthermore introduce anisotropic active stresses in the vertex model and analyze their effect on rheology. We include this anisotropy in the mean-field model and show that it recapitulates the behavior observed in the simulations. Our work clarifies how tissue rheology is related to stochastic cell rearrangements and provides a simple biophysical model to describe biological tissues. Further, it highlights the importance of nonlinearities when discussing tissue mechanics.

Automated summary

This study investigates the rheology of polygonal cellular networks using a vertex model, taking into account fluctuations. The research reveals nonlinear shear-thinning behavior in tissues under different magnitudes of fluctuations, with an even stronger nonlinear regime at lower values. A mean-field model successfully captures this nonlinear rheology by describing the tissue in terms of cell elongation and cell rearrangements, and introduces anisotropic active stresses to analyze their effect on rheology. Incorporating this anisotropy in the mean-field model replicates the behavior observed in simulations, providing insights into the relationship between tissue rheology and stochastic cell rearrangements.