Crosslinking and depletion determine spatial instabilities in cytoskeletal active matter

Active gels made of cytoskeletal proteins are valuable materials with attractive non-equilibrium properties such as spatial self-organization and self-propulsion. At least four typical routes to spatial patterning have been reported to date in different types of cytoskeletal active gels: bending and buckling instabilities in extensile systems, and global and local contraction instabilities in contractile gels. Here we report the observation of these four instabilities in a single type of active gel and we show that they are controlled by two parameters: the concentrations of ATP and depletion agent. We demonstrate that as the ATP concentration decreases, the concentration of passive motors increases until the gel undergoes a gelation transition. At this point, buckling is selected against bending, while global contraction is favored over local ones. Our observations are coherent with a hydrodynamic model of a viscoelastic active gel where the filaments are crosslinked with a characteristic time that diverges as the ATP concentration decreases. Our work thus provides a unified view of spatial instabilities in cytoskeletal active matter.