  Molecular-motor generated active stresses drive the cytoskeleton away from
equilibrium, endowing it with tunable mechanical properties that are essential
for diverse functions such as cell division and motility[1-5]. Designing
analogous biomimetic systems is a key prerequisite for creating active matter
that can emulate cellular functions[6-7]. These long-term goals requires
understanding of how motor-generated stresses tune the mechanics of filamentous
networks[8-11]. In microtubule-based active matter, kinesin motors generate
extensile motion that leads to persistent breaking and reforming of the network
links[12]. We study how such microscopic dynamics modifies the network's
mechanical properties, uncovering that the network viscosity first increases
with the imposed shear rate before transitioning back to a low-viscosity state.
The non-monotonic shear-dependent viscosity can be controlled by tuning the
speed of molecular motors. A two-state phenomenological model that incorporates
liquid- and solid-like elements quantitatively relates the non-monotonic
shear-rate-dependent viscosity to locally-measured flows. These studies show
that rheology of extensile networks are different from previously studied
active gels[13], where contractility enhances mechanical stiffness. Moreover,
the flow induced gelation is not captured by continuum models of
hydrodynamically interacting swimmers[14-21]. Observation of activity-dependent
viscoelasticity necessitates the development of models for self-yielding of
soft active solids whose intrinsic active stresses fluidize or stiffen the
network.
