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Abstract The cytoskeleton is an active composite of filamentous proteins that dictates diverse mechanical properties and processes in eukaryotic cells by generating forces and autonomously restructuring itself. Enzymatic motors that act on the comprising filaments play key roles in this activity, driving spatiotemporally heterogeneous mechanical responses that are critical to cellular multifunctionality, but also render mechanical characterization challenging. Here, we couple optical tweezers microrheology and fluorescence microscopy with simulations and mathematical modeling to robustly characterize the mechanics of active composites of actin filaments and microtubules restructured by kinesin motors. It is discovered that composites exhibit a rich ensemble of force response behaviors–elastic, yielding, and stiffening–with their propensity and properties tuned by motor concentration and strain rate. Moreover, intermediate kinesin concentrations elicit emergent mechanical stiffness and resistance while higher and lower concentrations exhibit softer, more viscous dissipation. It is further shown that composites transition from well‐mixed interpenetrating double‐networks of actin and microtubules to de‐mixed states of microtubule‐rich aggregates surrounded by relatively undisturbed actin phases. It is this de‐mixing that leads to the emergent mechanical response, offering an alternate route that composites can leverage to achieve enhanced stiffness through coupling of structure and mechanics. 

Abstract The cellular cytoskeleton relies on diverse populations of motors, filaments, and binding proteins acting in concert to enable nonequilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton's versatile reconfigurability, programmed by interactions between its constituents, makes it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate—far from the composite cytoskeleton in cells. Here, we engineer actin–microtubule (MT) composites, driven by kinesin and myosin motors and tuned by crosslinkers, to ballistically restructure and flow with speeds that span three orders of magnitude depending on the composite formulation and time relative to the onset of motor activity. Differential dynamic microscopy analyses reveal that kinesin and myosin compete to delay the onset of acceleration and suppress discrete restructuring events, while passive crosslinking of either actin or MTs has an opposite effect. Our minimal advection–diffusion model and spatial correlation analyses correlate these dynamics to structure, with motor antagonism suppressing reconfiguration and demixing, while crosslinking enhances clustering. Despite the rich formulation space and emergent formulation-dependent structures, the nonequilibrium dynamics across all composites and timescales can be organized into three classes—slow isotropic reorientation, fast directional flow, and multimode restructuring. Moreover, our mathematical model demonstrates that diverse structural motifs can arise simply from the interplay between motor-driven advection and frictional drag. These general features of our platform facilitate applicability to other active matter systems and shed light on diverse ways that cytoskeletal components can cooperate or compete to enable wide-ranging cellular processes.