Active-Nematic Defect Attractors on Curved Biological Surfaces

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. We further introduce a slow scalar material field representing generic biomaterial accumulation, stiffening, or reduced dynamic accessibility, showing how defect-mediated orientation patterns may become stabilised as material memory or mechanochemical lock-in.