Topological floppy modes in models of epithelial tissues

Area of Science:

• Mechanics
• Biophysics
• Materials Science

Background:

• Topological mechanics explains unique phenomena in mechanical networks.
• These phenomena include topologically protected floppy modes and states of self-stress localized at boundaries.
• In epithelial tissues, these modes may cause localized soft or stressed regions, influencing morphogenesis.

Purpose of the Study:

• To investigate the topological mechanics of epithelial tissues.
• To understand the role of boundary and interface modes in tissue mechanics and morphogenesis.
• To compare a vertex model (VM) with an active tension network (ATN) model.

Main Methods:

• Analysis of spatially periodic lattices at the Maxwell point of mechanical instability.
• Modeling epithelial tissues using a vertex model (VM) with effective elastic energy.
• Modeling using an active tension network (ATN) incorporating active cytoskeleton adaptation.

Main Results:

• Topologically polarized phases were identified in the active tension network (ATN).
• Exponential localization of floppy modes and states of self-stress was observed in the ATN.
• These topological effects occurred when cells were allowed to become concave.
• The vertex model (VM) did not exhibit these topological phenomena.

Conclusions:

• Active tension networks (ATN) exhibit topological polarization and localized modes when cells are concave.
• Concave cell shapes are crucial for observing topological phenomena in active epithelial tissues.
• Topological mechanics offers insights into localized stress and potential roles in morphogenesis.