Patterning of morphogenetic anisotropy fields

TL;DR

This paper presents a minimal model coupling morphogen gradients and nematic order to explain the organization of muscle fibers and defect formation in Hydra, reproducing observed developmental patterns on curved surfaces.

Contribution

It introduces a coupled model of morphogen gradients and nematic order that explains defect dynamics and tissue organization during Hydra development.

Findings

Gradient alignment induces defect unbinding during budding.

The model reproduces defect stabilization at Hydra's mouth.

Curved surface simulations match experimental reorganization patterns.

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.