  Many-body interactions in systems of active matter can cause particles to
move collectively and self-organize into dynamic structures with long-range
order. In cells, the self-assembly of cytoskeletal filaments is critical for
cellular motility, structure, intracellular transport, and division.
Semiflexible cytoskeletal filaments driven by polymerization or motor-protein
interactions on a two-dimensional substrate, such as the cell cortex, can
induce filament bending and curvature leading to interesting collective
behavior. For example, the bacterial cell-division filament FtsZ is known to
have intrinsic curvature that causes it to self-organize into rings and
vortices, and recent experiments reconstituting the collective motion of
microtubules driven by motor proteins on a surface have observed chiral
symmetry breaking of the collective behavior due to motor-induced curvature of
the filaments. Previous work on the self-organization of driven filament
systems have not studied the effects of curvature and filament structure on
collective behavior. In this work, we present Brownian dynamics simulation
results of driven semiflexible filaments with intrinsic curvature and
investigate how the interplay between filament rigidity and radius of curvature
can tune the self-organization behavior in homochiral systems and heterochiral
mixtures. We find a curvature-induced phase transition from polar flocks to
self-sorted chiral clusters, which is modified by filament flexibility. This
phase transition changes filament transport from ballistic to diffusive at long
timescales.
