Interplay of curvature and rigidity in shape-based models of confluent tissue

Abstract

Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity in two-dimensional vertex models confined to the surface of a sphere. By considering shapes of cells defined by perimeters whose magnitude depends on geodesic distances and areas determined by spherical polygons, the critical shape index in such models is affected by the size of the cell relative to the radius of the sphere on which it is embedded. This implies that cells can collectively rigidify by growing the size of the sphere, i.e. by tuning the curvature of their domain. Finite-temperature studies indicate that cell motility is affected well away from the zero-temperature transition point.

8 pages, 4 figures, fun numerical results

References in corpus (3)

• Active swarms on a sphere
• Fast, scalable, and interactive software for Landau-de Gennes numerical modeling of nematic topological defects
• 3D shape of epithelial cells on curved substrates

Cited by in corpus (8)

• Design of nematic liquid crystals to control microscale dynamics
• Soft Metamaterials: Adaptation and Intelligence
• Quantifying the link between local structure and cellular rearrangements using information in models of biological tissues
• Coordinated motion of epithelial layers on curved surfaces
• Effects of local curvature on epithelia tissue -- coordinated rotational movement and other spatiotemporal arrangements
• The cell adaptation time sets a minimum length scale for patterned substrates
• Shape driven confluent rigidity transition in curved biological tissues
• Substrate disorder promotes cell motility in confluent tissues