  Active fluids, such as cytoskeletal filaments, bacterial colonies and
epithelial cell layers, exhibit distinctive orientational coherence, often
characterized by nematic order and topological defects. By contrast, little is
known about positional coherence -- i.e., how a hidden dynamic skeleton
organizes the underlying chaotic motion -- despite this being one of their most
prominent and experimentally accessible features. Using a combination of
dynamical systems theory, experiments on two-dimensional mixtures of
microtubules and kinesin and hydrodynamic simulations, we characterize
positional coherence in active nematics. These coherent structures can be
identified in the framework of Lagrangian dynamics as moving attractors and
repellers, which orchestrate complex motion. To understand the interaction of
positional and orientational coherence on the dynamics of defects, we then
analysed observations and simulations and see that +1/2 defects move and deform
the attractors, thus functioning as control centers for collective motion.
Additionally, we find that regions around isolated +1/2 defects undergo high
bending and low stretching/shearing deformations, consistent with the local
stress distribution. The stress is minimum at the defect, while high
differential stress along the defect orientation induces folding. Our work
offers a new perspective to describe self-organization in active fluids, with
potential applications to multicellular systems.
