  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.
