General theory for the mechanics of confined microtubule asters

In cells, dynamic microtubules organize into asters or spindles to assist positioning of organelles. Two types of forces are suggested to contribute to the positioning process, (i) microtubule-growth based pushing forces and (ii) motor protein mediated pulling forces. In this paper, we present a general theory to account for aster positioning in a confinement of arbitrary shape. The theory takes account of microtubule nucleation, growth, catastrophe, slipping, as well as interaction with cortical force generators. We calculate microtubule distributions and forces acting on microtubule organizing centers in a sphere and in an ellipsoid. Positioning mechanisms based on both pushing forces and pulling forces can be distinguished in our theory for different parameter regimes or in different geometries. In addition, we investigate positioning of microtubule asters in the case of asymmetric distribution of motors. This analysis enables us to characterize situations relevant for Caenorrhabditis elegans embryos.