Nonlinear rheology of cellular networks

Abstract

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 meanfield 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.

Universality in the Mechanical Behavior of Vertex Models for Biological Tissues

“…Interestingly, in ordered ground states of the model, there is a distinction between the onset of rigidity determined by the shear modulus (which occurs at the shape index of a regular hexagon, p 0 ∼ 3.72), and when energy barriers disappear (at ). This suggests that there must be non-analytic cusps in the potential energy landscape Sussman and Merkel (2018 ); Popović et al (2021 ) and that there may be significant differences between the linear (zero strain rate, infinitesimal strain) and nonlinear (finite strain rate, finite strain) rheology of vertex models, which have recently been studied in 2D Duclut et al (2021 ); Basan et al (2011 ); Popović et al (2021 ) and 3D Sanematsu et al (2021 ).…”

Symmetry, Thermodynamics and Topology in Active Matter

“…These couplings play an essential role in the transmission of spatial information in large cell monolayers, which are often mediated by travelling waves, pulses, and a tug of war between cell-cell and cell-substrate forces [210,211]. While some recent progress has been made on incorporating these couplings in continuum models [212], informed by studies of mesoscopic models and by experiments, formulating an adaptive rheological model of tissue remains an open challenge. This is further complicated by the fact that living tissue is also capable of adapting its mechanical state in response to changes in environment, through feedback loops in a way that has so far largely eluded predictive theoretical descriptions.…”

Shear-driven solidification and nonlinear elasticity in epithelial tissues

“…A growing number of theoretical studies has begun to address this gap. Various groups have used vertex-based models [54,55] to simulate the linear [56,57] and nonlinear [58] rheology of a tissue under steady shear flow. The effects of active tension fluctuations [58,59] and cell division [60] have been explored.…”

“…Various groups have used vertex-based models [54,55] to simulate the linear [56,57] and nonlinear [58] rheology of a tissue under steady shear flow. The effects of active tension fluctuations [58,59] and cell division [60] have been explored. An earlier study [61] has also showed that the vertex model can reproduce a nonlinear mechanical response qualitatively similar to that observed experimentally [37].…”