Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model

Abstract

Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. The model predicts that mechanical interactions can generate mesoscopic patterns within the monolayer that exhibit long-range correlations in cell shape. The model also suggests that the orientation of mechanical and geometric cues for processes such as cell division are likely to be strongly correlated in real epithelia. Some limitations of the model in capturing geometric features of Xenopus epithelial cells are highlighted.

29 pages, 10 figures, revision

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Cited by in corpus (9)

• Linear Viscoelastic Properties of the Vertex Model for Epithelial Tissues
• Mechanical characterization of disordered and anisotropic cellular monolayers
• Linear Viscoelastic Response of the Vertex Model with Internal and External Dissipation: Normal Modes Analysis
• Couple stresses and discrete potentials in the vertex model of cellular monolayers
• Force networks, torque balance and Airy stress in the planar vertex model of a confluent epithelium
• Spectral approaches to stress relaxation in epithelial monolayers
• Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth
• Geometry of T1 transitions in epithelia
• Mechanically-driven growth and competition in a Voronoi model of tissues