Morphogenesis driven by nematic defects in active biological networks

Abstract

Cellular morphogenesis, the process by which biological tissues acquire shape and structure, remains a fundamental challenge in understanding pattern formation and the coordinated remodeling of cellular assemblies. Under appropriate conditions, cytoskeletal filaments can organize into a nematic phase exhibiting partial orientational order. Topological defects within this nematic organization generate localized mechanical stresses that destabilize the tissue and promote deformation and structural rearrangements to relieve internal stresses. We develop a continuum framework that models living tissues as active biological networks represented as nematic polymer networks capable of heterogeneous growth and remodeling. The model captures macroscopic effects through spatial variations in the fiber order parameter which drives the system away from equilibrium. Morphogenesis is described as a sequence of quasi-static equilibrium states governed by the coupling between nematic order, elasticity, stress-driven growth, and adaptive relaxation. Finite element simulations illustrate Hydra regeneration and development when topological defects are prescribed according to the mature organism's expected morphology. The results show that defect topology controls stress localization and shape evolution: $+1$ defects drive protrusion formation, while $-1/2$ defects act as structural stabilizers with minimal growth. By varying the initial defect configuration, we model diverse morphogenetic outcomes, including uniaxial regeneration, tentacle formation, and biaxial development.