  The plant microtubule cortical array is a striking feature of all growing
plant cells. It consists of a more or less homogeneously distributed array of
highly aligned microtubules connected to the inner side of the plasma membrane
and oriented transversely to the cell growth axis. Here we formulate a
continuum model to describe the origin of orientational order in such confined
arrays of dynamical microtubules. The model is based on recent experimental
observations that show that a growing cortical microtubule can interact through
angle dependent collisions with pre-existing microtubules that can lead either
to co-alignment of the growth, retraction through catastrophe induction or
crossing over the encountered microtubule. We identify a single control
parameter, which is fully determined by the nucleation rate and intrinsic
dynamics of individual microtubules. We solve the model analytically in the
stationary isotropic phase, discuss the limits of stability of this isotropic
phase, and explicitly solve for the ordered stationary states in a simplified
version of the model.
