  Building on the striking similarity between the structure of the spindle
during mitosis in living cells and nematic textures in confined liquid
crystals, we use a continuum model of two-dimensional nematic liquid crystal
droplets, to examine the physical aspects of cell division. The model
investigates the interplay between bulk elasticity of the microtubule assembly,
described as a nematic liquid crystal, and surface elasticity of the cell
cortex, modelled as a bounding flexible membrane, in controlling cell shape and
division. The centrosomes at the spindle poles correspond to the cores of the
topological defects required to accommodate nematic order in a closed geometry.
We map out the progression of both healthy bipolar and faulty multi-polar
division as a function of an effective parameter that incorporates active
processes and controls centrosome separation. A robust prediction, independent
of energetic considerations, is that the transition from a single cell to
daughters cells occurs at critical value of this parameter. Our model
additionally suggests that microtubule anchoring at the cell cortex may play an
important role for successful bipolar division. This can be tested
experimentally by regulating microtubule anchoring.
