Pattern formation in active model C: bands, aster networks, and foams

We study the dynamics of pattern formation in a minimal model for active mixtures made of biofilaments and molecular motors. In particular, we monitor the evolution of the conserved density of filaments and of the non-conserved nematic order parameter, focusing on the effects of an "anchoring" term that provides a direct coupling between the preferred filament direction and their density gradient. The key control parameter is the ratio between activity and elasticity. When elasticity dominates, the interplay between activity and anchoring leads to the formation of banded structures that can undergo additional bending or rotational instabilities. When activity dominates, the nature of anchoring instead gives rise to a range of active cellular solids, including aster-like networks, and disordered foams. We speculate that the introduced "active model C" with anchoring is a minimal model to describe pattern formation in a biomimetic analog of the cytoskeleton. Finally, we demonstrate how the modified active model C can be applied for the investigation of spindle-like structures occurring during the cell division.