Geometry of T1 transitions in epithelia

Area of Science:

• Physics and Biophysics
• Cell Biology
• Materials Science

Background:

• Epithelial tissue flows are fundamental to development and wound healing.
• T1 transitions, or neighbor exchanges, are key cellular rearrangements driving tissue dynamics.
• These rearrangements are characterized by an energy barrier influenced by cell geometry and physical forces.

Purpose of the Study:

• To precisely determine the energy barrier for isolated T1 transitions in epithelial tissues.
• To investigate the impact of deviations in cell packing and line tension fluctuations on this energy barrier.
• To analyze the role of nonlinear tensions in vertex models concerning T1 transition resistance.

Main Methods:

• Exact geometric construction to calculate the energy barrier for T1 transitions.
• Analysis of how variations in cell packing affect the energy barrier.
• Investigation of line tension fluctuations and their average effect on the barrier.
• Geometric proof to demonstrate resistance to T1 transitions by nonlinear tensions in vertex models.

Main Results:

• The energy barrier for T1 transitions is determined by line tensions.
• Deviations from regular cell packing reduce the energy barrier.
• Line tension fluctuations increase the energy barrier on average.
• Nonlinear tensions in vertex models inherently resist T1 transitions.

Conclusions:

• This work provides an exact quantification of the energy barrier for T1 transitions.
• The findings elucidate how cell packing irregularities and tension dynamics modulate tissue rearrangement energetics.
• Results offer a foundation for developing continuum models of epithelial tissue dynamics and cell migration.