  The dynamic patterning of the plant hormone auxin and its efflux facilitator
the PIN protein are the key regulator for the spatial and temporal organization
of plant development. In particular auxin induces the polar localization of its
own efflux facilitator. Due to this positive feedback auxin flow is directed
and patterns of auxin and PIN arise. During the earliest stage of vein
initiation in leaves auxin accumulates in a single cell in a rim of epidermal
cells from which it flows into the ground meristem tissue of the leaf blade.
There the localized auxin supply yields the successive polarization of PIN
distribution along a strand of cells. We model the auxin and PIN dynamics
within cells with a minimal canalization model. Solving the model analytically
we uncover an excitable polarization front that triggers a polar distribution
of PIN proteins in cells. As polarization fronts may extend to opposing
directions from their initiation site we suggest a possible resolution to the
puzzling occurrence of bipolar cells, such we offer an explanation for the
development of closed, looped veins. Employing non-linear analysis we identify
the role of the contributing microscopic processes during polarization.
Furthermore, we deduce quantitative predictions on polarization fronts
establishing a route to determine the up to now largely unknown kinetic rates
of auxin and PIN dynamics.
