  Actomyosin networks are major structural components of the cell. They provide
mechanical integrity and allow dynamic remodeling of eukaryotic cells,
self-organizing into the diverse patterns essential for development. We provide
a theoretical framework to investigate the intricate interplay between local
force generation, network connectivity and collective action of molecular
motors. This framework is capable of accommodating both regular and
heterogeneous pattern formation, arrested coarsening and macroscopic
contraction in a unified manner. We model the actomyosin system as a motorized
cat's cradle consisting of a crosslinked network of nonlinear elastic filaments
subjected to spatially anti-correlated motor kicks acting on motorized (fibril)
crosslinks. The phase diagram suggests there can be arrested phase separation
which provides a natural explanation for the aggregation and coalescence of
actomyosin condensates. Simulation studies confirm the theoretical picture that
a nonequilibrium many-body system driven by correlated motor kicks can behave
as if it were at an effective equilibrium, but with modified interactions that
account for the correlation of the motor driven motions of the actively bonded
nodes. Regular aster patterns are observed both in Brownian dynamics
simulations at effective equilibrium and in the complete stochastic
simulations. The results show that large-scale contraction requires correlated
kicking.
