Patterning of morphogenetic anisotropy fields

Abstract

Orientational order, encoded in anisotropic fields, plays an important role during the development of an organism. A striking example of this is the freshwater polyp Hydra, where topological defects in the muscle fiber orientation have been shown to localize to key features of the body plan. This body plan is organized by morphogen concentration gradients, raising the question how muscle fiber orientation, morphogen gradients and body shape interact. Here, we introduce a minimal model that couples nematic orientational order to the gradient of a morphogen field. We show that on a planar surface alignment to a radial concentration gradient can induce unbinding of topological defects, as observed during budding and tentacle formation in Hydra, and stabilize aster/vortex-like defects, as observed at a Hydra's mouth. On curved surfaces mimicking the morphologies of Hydra in various stages of development -- from spheroid to adult -- our model reproduces the experimentally observed reorganization of orientational order. Our results suggest how gradient alignment and curvature effects may work together to control orientational order during development and lays the foundations for future modeling efforts that will include the tissue mechanics that drive shape deformations.

arXiv commentv2: Published version with minor revisions. v1: 12 pages, 7 figures (4 main, 3 suppl.). Movies: https://youtube.com/playlist?list=PLdejNN8-Lt6HJ52YfhyegpI0PGoRq8pSb

References in corpus (17)

• Topological defect launches 3D mound in the active nematic sheet of neural progenitors
• The Geometry of Soft Materials: A Primer
• Two-Dimensional Matter: Order, Curvature and Defects
• Topological defects promote layer formation in Myxococcus xanthus colonies
• Vortices in Superfluid Films on Curved Surfaces
• Topological Defects in Spherical Nematics
• Crystallography on Curved Surfaces
• Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals
• Theory of defect-mediated morphogenesis
• Topology and morphology of self-deforming active shells
• A finite element approach for vector- and tensor-valued surface PDEs
• Defect generation and deconfinement on corrugated topographies
• Orientational order on surfaces - the coupling of topology, geometry, and dynamics
• Active nematic defects and epithelial morphogenesis
• Active morphogenesis of patterned epithelial shells
• Defective nematogenesis: Gauss curvature in programmable shape-responsive sheets with topological defects
• Cooling a spherical nematic shell

Cited by in corpus (8)

• Exact and approximate solutions for elastic interactions in a nematic liquid crystal
• Mechanochemical Topological Defects in an Active Nematic
• Density-polarity coupling in confined active polar films: asters, spirals, and biphasic orientational phases
• Cells around the corner
• Stabilization of active tissue deformation by a dynamic signaling gradient
• Active Filaments on Curved Surfaces: From Single Filaments to Dilute Suspensions
• The importance of being discrete -- An agent-based model for active nematics and more
• Defect binding-unbinding transition in active nematic membranes