Self-Organization of Microtubules and Molecular Motors

One of the central questions in biology concerns the formation of complex, highly organized microscopic structures from initially disordered states. Complex ordered structures are established and maintained through a dynamic interplay between self-assembly and regulatory processes.

Here, we introduce a model for spatio-temporal self-organization of an ensemble of microtubules interacting via molecular motors. Starting from a generic stochastic model of inelastic polar rods with an anisotropic interaction kernel, we derive a set of equations for the concentration and orientation of the local rods. At a large enough mean density of rods and concentration of motors, the model describes orientational instability. We demonstrate that orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters, as seen in recent experiments. The corresponding phase diagram of vortex-aster transitions is in qualitative agreement with the experiment.