  The cytoskeleton relies on diverse populations of motors, filaments, and
binding proteins acting in concert to enable non-equilibrium processes ranging
from mitosis to chemotaxis. Its versatile reconfigurability, programmed by
interactions between its constituents, make the cytoskeleton foundational
active matter. Yet, 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
double-networks, 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
microtubules has an opposite effect. Our minimal advection-diffusion model and
spatial correlation analyses correlate these dynamics to structure, with motor
antagonism suppressing reconfiguration and de-mixing, while crosslinking
enhances clustering. Despite the rich formulation space and emergent
formulation-dependent structures, the non-equilibrium dynamics across all
networks 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.
