Instabilities and Geometry of Growing Tissues

Area of Science:

• Biophysics
• Soft Matter Physics
• Cellular Mechanics

Background:

• Epithelial tissues exhibit complex mechanical behaviors influenced by cellular properties and tissue geometry.
• Understanding tissue instabilities and homeostatic states is crucial for developmental biology and tissue engineering.

Purpose of the Study:

• To develop a covariant continuum formulation for a generalized 2D vertex model of epithelial tissues.
• To analytically describe tissue mechanics, including instabilities and elastic/plastic responses.
• To investigate the role of cell-shape heterogeneity and residual stresses on tissue behavior.

Main Methods:

• Utilized a geometrical approach combined with out-of-equilibrium statistical mechanics.
• Formulated a covariant continuum model for vertex-like tissue structures.
• Calculated mechanical and dynamical instabilities, and cell pressure in homeostatic states.

Main Results:

• Identified dependencies of mechanical and dynamical instabilities on tissue activity and cell-shape heterogeneity.
• Demonstrated that plastic cellular rearrangements and elastic response are linked to mechanical residual stresses.
• Showed that freely growing tissues can experience growth instability based on proliferation rates.
• Explicitly calculated homeostatic cell pressure in confined growing tissues, revealing it can be negative and stress-dependent.

Conclusions:

• The geometric model successfully separates elastic and plastic effects in growing, flowing tissues.
• Mechanical residual stresses play a significant role in both cellular rearrangements and overall tissue response.
• The model provides a framework for understanding tissue self-organization and stability under various conditions.