Self-organization of microtubules interacting with molecular motors and crosslinks
Igor Aronson
Materials Science Division
Argonne National Laboratory
A central question in biology concerns the origin of highly-organized self-assembled macroscopic structures from initially disordered states. The mixture of long and rigid microtubules and dynamic molecular motors constitutes a unique well-controlled system which is relavant to a variery of applications, from self-assembeld biosensors to biomemetic materials. In vitro experiments on self-assembly of motors and microtubules in quasi-two-dimensional geometry revealed a variety of spontaneous large-scale patterns: ray-like asters, rotating vortices and filament bundles. Motivated by these experiments, we derive from microscopic interaction rules a model describing spatio-temporal organization of an array of microtubules interacting with dynamic molecular motors and static crosslinks. Starting from a generic stochastic microscopic model of inelastic polar rods, we obtain a set of equations for the local rods concentration and orientation. Above a certain critical density of the rods, the model exhibits spontaneous orientational phase transition and the onset of large-scale coherence. We demonstrate that this orientational transition leads to the formation of vortices, asters, and bundles seen in recent experiments.