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Active matter systems evade the constraints of thermal equilibrium, leadingto the emergence of intriguing collective behavior. A paradigmatic example isgiven by motor-filament mixtures, where the motion of motor proteins drivesalignment and sliding interactions between filaments and theirself-organization into macroscopic structures. After defining a microscopicmodel for these systems, we derive continuum equations, exhibiting theformation of active supramolecular assemblies such as micelles, bilayers andfoams. The transition between these structures is driven by a branchinginstability, which destabilizes the orientational order within the micelles,leading to the growth of bilayers at high microtubule densities. Additionally,we identify a fingering instability, modulating the shape of the micelleinterface at high motor densities. We study the role of various mechanisms inthese two instabilities, such as contractility, active splay, and anchoring,allowing for generalization beyond the system considered here.

Supramolecular assemblies in active motor-filament systems: micelles, bilayers, and foams