Theory of epithelial elasticity

Area of Science:

• Biophysics
• Cell Biology
• Materials Science

Background:

• Epithelial monolayers form complex 3D structures through tissue morphogenesis.
• Understanding the mechanical forces governing these shape changes is crucial for developmental biology and disease modeling.

Purpose of the Study:

• To develop an elastic theory for epithelial monolayers using a discrete cell model.
• To investigate the relationship between differential cell surface tensions and tissue morphology, specifically folding.
• To identify mechanisms stabilizing tissue folds and explore the coupling between monolayer thickness and curvature.

Main Methods:

• A two-dimensional discrete model of droplet-like cells with differential surface tensions (apical, basal, lateral).
• Analysis of effective tissue bending modulus and its dependence on apicobasal differential tension.
• Investigation of fold stabilization mechanisms: cell geometry constraints, cell-cell interactions, and basement membrane elasticity.
• Modeling of monolayer thickness variation and its coupling with curvature.

Main Results:

• The effective tissue bending modulus depends on apicobasal differential tension and dictates the transition from flat to folded states.
• Three mechanisms (cell geometry, cell interactions, basement membrane elasticity) stabilize finite-wavelength folds.
• Monolayer thickness varies along the waveform and is coupled to curvature, governed by apicobasal polarity.
• Thickness modulation amplitude correlates with apicobasal differential tension, suggesting indirect stress measurement.

Conclusions:

• Apicobasal differential tension is a critical factor in epithelial monolayer folding and thickness modulation.
• Easily measurable morphometric parameters can indirectly indicate intracellular stresses.
• The developed elastic theory provides a framework for understanding tissue morphogenesis and mechanics.