Positioning of microtubule (MT) organizing centers with respect to the confining geometry of cells depends on pushing and/or pulling forces generated by MTs that interact with the cell cortex (Dogterom et al 2005 Curr. Opin. Cell Biol. 17 67–74). How, in living cells, these forces lead to proper positioning is still largely an open question. Recently, it was shown by in vitro experiments using artificial microchambers that in a square geometry, MT asters center more reliably by a combination of pulling and pushing forces than by pushing forces alone (Laan et al 2012a Cell 148 502–14). These findings were explained by a physical description of aster mechanics that includes slipping of pushing MT ends along chamber boundaries. In this paper, we extend that theoretical work by studying the influence of the shape of the confining geometry on the positioning process. We find that pushing and pulling forces can have centering or off-centering behavior in different geometries. Pushing forces center in a one- dimensional and a square geometry, but lead to off-centering in a circle if slipping is sufficiently pronounced. Pulling forces, however, do not center in a one-dimensional geometry, but improve centering in a circle and a square. In an elongated stadium geometry, positioning along the short axis depends mainly on pulling forces, while positioning along the long axis depends mainly on pushing forces. Our theoretical results suggest that different positioning strategies could be used by different cell types.
