Landscape of Metastable States for Epithelial Tissue Monolayers

Recent work on Madin-Darby Canine Kidney II cells has developed a quantitative understanding of the importance of three-dimensional effects in the elastic mechanics of single-layer tissues. The associated continuum shell modeling motivates an effective 2D vertex model with significant differences to traditional vertex modeling: anharmonic elasticity and anisotropic elasticity due to basal actin stress fibers.

We conduct simulations of disordered confluent tissues obeying the new 2D model and analyze the landscape of its metastable energy states in order to elucidate whether geometric and statistical morphological indicators that are successful predictors of energy and stability in the traditional vertex models remain valid. We find that statistical measures are insensitive to the modeling changes, while the geometric index of perimeter lengths increases specifically because of anisotropic actin mechanics. With information about the average strength of contractile actin in the tissue, predictability of position on the energy landscape can thus be restored. By contrast, the introduction of anharmonic elasticity dramatically shifts the predicted location of the loss-of-rigidity transition point, and influences our thinking on the tradeoff between tissue cohesion and tissue stiffness.