Tuneable defect-curvature coupling and topological transitions in active shells.

Area of Science:

• Biophysics
• Soft Matter Physics
• Developmental Biology

Background:

• Topological defects are known to influence geometry in passive liquid crystals.
• The role of biological activity in defect-mediated morphogenesis is largely unexplored.
• Understanding active matter is crucial for explaining complex biological processes.

Purpose of the Study:

• To investigate the role of activity in the mechanical coupling between topological defects and curvature in deformable shells.
• To explore how different types of active liquid crystals (polar and nematic) and defect structures (asters, vortices) affect this coupling.
• To determine if activity can drive significant topological transitions in biological structures.

Main Methods:

• Linear stability analysis to probe the behavior of active liquid crystal shells.
• Three-dimensional computational fluid dynamics simulations to model defect dynamics and shell deformation.
• Analysis of the interplay between liquid crystal order, defect type, and active forces.

Main Results:

• Active liquid crystals exhibit a more complex and versatile coupling between defects and curvature than passive systems.
• The nature of the active forces and defect structure (asters vs. vortices) significantly tune this mechanical coupling.
• In polar active liquid crystals with high extensile activity, a transition from spherical to toroidal topology is observed.

Conclusions:

• Topological defects can act as 'topological morphogens' in active systems, guiding embryonic development.
• The findings provide a theoretical framework for understanding defect-driven shape changes in active biological matter.
• The study offers testable predictions for in vitro experiments, particularly in organoid development.