Polar auxin transport dynamics of primary and secondary vein patterning in dicot leaves

The growth regulator auxin plays a central role in the phyllotaxy, shape, and venation patterns of leaves. The auxin spatial localization underlying these phenomena involves polar auxin transport (PAT) at the cellular level, particularly the preferential allocation of PIN efflux proteins to certain areas of the plasma membrane. Two general mechanisms have been studied: an up-the-gradient (UTG) allocation dependent on neighbouring-cell auxin concentrations, and a with-the-flux (WTF) allocation dependent on the flow of auxin across walls. We have developed a combined UTG+WTF model to quantify the observed auxin flows both towards (UTG) and away from (WTF) auxin maxima during primary and secondary vein patterning in leaves. The model simulates intracellular and membrane kinetics and intercellular transport, and is solved for a 2D leaf of several hundred cells. In addition to normal development, modelling of increasing PAT inhibition generates, as observed experimentally: a switch from several distinct vein initiation sites to many less-distinct sites; a delay in vein canalization; inhibited connection of new veins to old; and finally loss of patterning in the margin, loss of vein extension, and confinement of auxin to the margin. The model generates the observed formation of discrete auxin maxima at leaf vein sources and shows the dependence of secondary vein patterning on the efficacy of auxin flux through cells. Simulations of vein patterning and leaf growth further indicate that growth itself may bridge the spatial scale from the cell-cell resolution of the PIN-auxin dynamics to vein patterns on the whole-leaf scale.