Microtubule patterning in the presence of moving motor proteins.

Cytoskeletal polymers such as microtubules (MTs) interact with motor proteins to form higher-order structures. In vitro experiments have shown that MT patterns such as asters, bundles, and vortices can form under the influence of a single type of dynamic motor protein. MTs also can form anti-parallel bundles, similar to bundles that form the mitotic spindle during cell division, under the influence of two types of moving motors with opposite directionality. Despite the importance of MT structures, their mechanism of formation is not yet understood. We develop an integro-partial differential equation model to describe the dynamic interactions between MTs and moving motor proteins. Our model takes into account motor protein speed, processivity, density, and directionality, as well as MT treadmilling and reorganization due to interactions with motors. Simulation results show that plus-end directed motor proteins can form vortex patterns at low motor density, while minus-end directed motor proteins form aster patterns at similar densities. Also, motor proteins with opposite directionality are able to organize MTs into anti-parallel bundles. Our model is able to provide a quantitative and qualitative description of MT patterning, providing insights into possible mechanisms of spindle formation.