Active nematic defects and epithelial morphogenesis

Abstract

Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. Applying this framework to the dynamics of cultured murine neural progenitor cells (NPCs) in an ex-vivo setting, we find that cells accumulate at positive defects and are depleted at negative defects. In contrast, applying this to the dynamics of a basal marine invertebrate \emph{Hydra} in an in-vivo setting, we show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles, consistent with observations.

11 pages, 4 figures. v2: minor edits

References in corpus (5)

• Spontaneous motion in hierarchically assembled active matter
• Theory of defect-mediated morphogenesis
• Defects in nematic membranes can buckle into pseudospheres
• Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations
• Defect Dynamics in Active Polar Fluids vs. Active Nematics

Cited by in corpus (17)

• Theory of defect-mediated morphogenesis
• Mechanical basis and topological routes to cell elimination
• Patterning of morphogenetic anisotropy fields
• Spontaneous Self-Constraint in Active Nematic Flows
• Morphodynamics of Active Nematic Fluid Surfaces
• Microdomains and Stress Distributions in Bacterial Monolayers on Curved Interfaces
• Spontaneous rotation of active droplets in two and three dimensions
• Tuneable defect-curvature coupling and topological transitions in active shells
• Defect absorption and emission for $p$-atic liquid crystals on cones
• Exact and approximate solutions for elastic interactions in a nematic liquid crystal
• Mechanochemical Topological Defects in an Active Nematic
• Active topological defect absorption by a curvature singularity
• Active Filaments on Curved Surfaces: From Single Filaments to Dilute Suspensions
• Motility and self propulsion of active droplets
• Spontaneous flow created by active topological defects
• Topological defects in polar active matter
• Defect binding-unbinding transition in active nematic membranes