The role of auxin transport through plasmodesmata in leaf vein canalization and patterning

Vein patterns in plant leaves are preceded by high concentration localized tracks of the phytohormone auxin. Auxin regulates downstream genes involved in vascular differentiation. Proposals for the mechanisms by which auxin canalizes from broad early distributions to later narrow provascular tracks have been made for many decades and tested in mathematical models. These have focused on PIN1, a membrane-bound protein involved in exporting auxin from cells. PIN mutations and interference with polar auxin transport (PAT) through PIN have strong effects on vein patterns. However, recent experiments show that even with PIN-dependent PAT presumably shut off, veins form and extend, albeit with altered patterning. This residual canalization and vein patterning has a dependence on flow through plasmodesmata (PD) intercellular channels. We developed a new mathematical framework for the regulation of auxin flow through both PIN and PD. This produces better fits to data than prior PIN-only models, especially with respect to vein number, directionality and extension in reduced PIN transport conditions. Varying PD area recapitulates known experimental results with PD mutants, in particular the loss of canalization at high PD permeability. Model parameters are consistent with measured permeabilities and predict effects for future experiments. This work updates the canalization hypothesis for auxin provascular strand formation in early leaf development in terms of the contributions from both PIN and PD.