Macroscopic equations for pattern formation in mixtures of microtubules and motors

Inspired by patterns observed in mixtures of microtubules and molecular motors, we propose continuum equations for the evolution of motor density, and microtubule orientation. The chief ingredients are the transport of motors along tubules, and the alignment of tubules in the process. The macroscopic equations lead to aster and vortex patterns in qualitative agreement with experiments. While the early stages of evolution of tubules are similar to coarsening of spins following a quench, the rearrangement of motors leads to arrested coarsening at low densities. Even in one dimension, the equations exhibit a variety of interesting behaviors, such as symmetry breaking, moving fronts, and motor localization.