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

We study the dynamics of pattern formation in a minimal model for active mixtures made of microtubules and molecular motors. We monitor the evolution of the (conserved) microtubule density and of the (non-conserved) nematic order parameter, focusing on the effects of an "anchoring" term that provides a direct coupling between the preferred microtubule 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 formation of banded structures that can undergo additional bending, rotational or splaying instabilities. When activity dominates, the nature of anchoring instead gives rise to a range of active cellular solids, including aster-like networks, disordered foams and spindle-like patterns. We speculate that the introduced "active model C" with anchoring is a minimal model to describe pattern formation in a biomimetic analogue of the microtubule cytoskeleton.