A variational method for image-based inference of internal stress in epithelial tissues

Area of Science:

• Cellular and developmental biology
• Biophysics
• Quantitative biology

Background:

• Epithelial morphogenesis relies on cellular mechanics, but in-vivo stress measurement is challenging.
• Existing image-based methods for stress inference are sensitive to errors and require precise segmentation.
• Understanding tissue mechanics is crucial for developmental biology and disease research.

Purpose of the Study:

• To introduce a novel, robust method for non-destructive stress inference in epithelial tissues.
• To overcome limitations of existing stress measurement techniques in live tissues.
• To provide quantitative insights into cellular mechanics during morphogenesis.

Main Methods:

• Developed the Variational Method of Stress Inference (VMSI) based on the duality between stress and geometry in discrete mechanical networks.
• Modeled epithelial apical geometry using 2D tilings of Circular Arc Polygons (CAPs).
• Applied VMSI to images of epithelial monolayers, simultaneously approximating geometry and internal forces under equilibrium constraints.

Main Results:

• VMSI demonstrated greater robustness compared to previous methods.
• VMSI predictions of cellular and mesoscopic stress in *Drosophila* embryogenesis correlated strongly (80%) with measured myosin II patterns.
• Analysis revealed myosin activity primarily contributes to static internal force balance within the epithelial layer.

Conclusions:

• VMSI offers a practical and non-destructive approach for estimating stress in live epithelial tissues.
• The method provides valuable insights into cell mechanics and force balance during tissue development.
• Accurate stress inference is key to understanding epithelial morphogenesis and related biological processes.