Tug-of-war between stretching and bending in living cell sheets

Area of Science:

• Physics
• Materials Science
• Biophysics

Background:

• Thin elastic sheets exhibit shape transitions dominated by stretching or bending deformations.
• Living epithelial tissues show spontaneous out-of-plane curling due to asymmetric surface stresses.
• This curling induces in-plane stretching, suggesting a competition between bending and stretching at tissue margins.

Purpose of the Study:

• To theoretically model the competition between stretching and bending in thin elastic sheets with active pre-strain and spontaneous curvature.
• To investigate how asymmetric surface stresses influence the 3D morphology of tissue margins.

Main Methods:

• Utilized the framework of non-Euclidean plates to extend the theory of thin elastic shells.
• Incorporated active pre-strain and spontaneous curvature into the theoretical model.
• Analyzed the scaling of stretching and bending energies in the limit of vanishing thickness.

Main Results:

• Demonstrated that spontaneous curvature scaling with 1/e leads to comparable stretching and bending energies.
• Showed that both energies compete to define the 3D shape of the tissue.
• Revealed that external tension continuously alters this competition.

Conclusions:

• The interplay between bending and stretching, driven by spontaneous curvature and influenced by external tension, governs the shape of tissue margins.
• This competition is crucial for understanding the morphology of biological tissues and engineered elastic materials.