Torques within microtubule bundles generate the curved shape of the mitotic spindle*

The mitotic spindle is a complex micro-machine made up of microtubules and associated proteins, which are highly ordered in space and time to ensure its proper biological functioning. A functional spindle has a characteristic shape, which includes curved bundles of microtubules that are twisted around the pole-to-pole axis. An in-depth understanding of both how the linear and rotational forces define the overall shape of the mitotic spindle and how the twisted shapes arise as a result of interactions between microtubules and motor proteins is still unclear. To answer this, we introduce a mean-field approach, in which we describe the dominating forces and torques at the poles, in order to model he entire spindle. The model also includes motor proteins which generate forces and torques within the antiparallel overlap region of microtubule bundles. By comparing theoretical results with experimentally observed shapes of bundles in the mitotic spindle, the model predicts that the shape of the entire spindle is predominately determined by rotational forces, and that a difference in bending forces explains the disparity in the shapes of inner and outer bundles.