Defect Attractors on Curved Biological Surfaces - A Minimal Active-Nematic Proof-of-Concept Framework

Biological surfaces often exhibit persistent orientation patterns, including whorls, spirals, ridges, and anisotropic fibre arrangements. Such structures are usually interpreted through developmental, genetic, or clinical frameworks. Here we present a qualitative proof-of-concept framework exploring whether a minimal physical description based on active nematic theory can reproduce key structural features of such patterns on curved biological surfaces. We do not model any specific biological system; the aim is to demonstrate minimal sufficiency rather than quantitative biological realism.We model orientation as a nematic order parameter on a curved manifold using a complex order-parameter equation within the complex Ginzburg–Landau universality class. Within this reduced framework, topological constraints, active dynamics, spatial stiffness gradients, and mechanochemical feedback generate spiral defect structures, curvature-dependent defect positioning, and localised scalar accumulation. The simulations suggest that topological defects can act as organising attractors: near-uniform orientation states on closed curved surfaces become dynamically unstable and evolve toward defect-containing configurations, consistent with a dynamical interpretation of the hairy-ball constraint.A robustness test using a minimally polar tangent-field extension — in which individual orientations carry directional rather than axial symmetry — confirms that defect formation and gradient-biased localisation persist when phase normalisation is removed, nonlinear saturation is retained, and the surface Laplacian is approximated by cotangent weights on triangulated spherical meshes. This polar extension should be interpreted as testing the persistence of defect-mediated organisation under a symmetry-extended implementation, not as a replacement for the nematic core model.Rather than proposing new physical laws or a validated biomedical model, this work identifies a minimal set of ingredients capable of producing biologically suggestive orientation, accumulation, and release patterns. The framework links active matter physics and mechanobiological growth, while generating testable predictions about defect localisation, spiral chirality, anisotropic propagation, and structural persistence.