Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

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 ows 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.