  In cells, cytoskeletal filament networks are responsible for cell movement,
growth, and division. Filaments in the cytoskeleton are driven and organized by
crosslinking molecular motors. In reconstituted cytoskeletal systems, motor
activity is responsible for far-from-equilibrium phenomena such as active
stress, self-organized flow, and spontaneous nematic defect generation. How
microscopic interactions between motors and filaments lead to larger-scale
dynamics remains incompletely understood. To build from motor-filament
interactions to predict bulk behavior of cytoskeletal systems, more
computationally efficient techniques for modeling motor-filament interactions
are needed. Here we derive a coarse-graining hierarchy of explicit and
continuum models for crosslinking motors that bind to and walk on filament
pairs. We compare the steady-state motor distribution and motor-induced
filament motion for the different models and analyze their computational cost.
All three models agree well in the limit of fast motor binding kinetics.
Evolving a truncated moment expansion of motor density speeds the computation
by $10^3$--$10^6$ compared to the explicit or continuous-density simulations,
suggesting an approach for more efficient simulation of large networks. These
tools facilitate further study of motor-filament networks on micrometer to
millimeter length scales.
