Globally ordered states in the collective motions of self-propelled, semi-flexible, penetrable filaments.

Gliding assays, in which cytoskeletal filaments translate over a substrate containing motor proteins, offer an experimental model system for studying the collective motions of self-propelled, anisotropic units. A wealth of active phases has been reported, characterized by orientational order that may be local or global, polar or nematic (apolar), and involving significant bending and crossovers when filaments collide. To elucidate the connection between these macroscopic and microscopic observations, we use Brownian dynamics simulations to study the collective motions of semi-flexible filaments that self-propel with a constant force along the local tangent direction. Crossovers are modeled with a finite energetic penalty for overlap. We focus on a high-density, high-penetrability regime where global orientational order emerges. Our results suggest that a globally ordered active nematic (apolar) state is transient, and the systems' steady state is instead a globally ordered active polar state. We find that the time required to saturate the global polar order increases with increasing stiffness of the active filaments.