Schematic representations of models.
(A) In Model O, auxin is transported between neighboring cells by PIN1, while PIN1 is polarized depending on auxin concentration of neighboring cells. (B) In Model A, auxin is transported between cytoplasm and apoplast by PIN1 and influx carrier, while PIN1 is polarized depending on auxin concentration of neighboring apoplast spaces. (C) In the framework of Model B, an assumed molecule X is incorporated into Model A. Molecule X is expressed in response to cytosolic auxin and diffuses freely between cytoplasm and apoplast. (D) Model B considers various feedback regulations from molecule X to auxin–PIN1 dynamics. (E) In Model B6, PIN1 is polarized depending on X concentration of neighboring apoplast spaces, instead of auxin. (F) In addition to simple diffusion between cytoplasm and apoplast, Models A and B consider direct diffusions between neighboring cells (symplast diffusion) and between neighboring apoplast spaces (apoplast diffusion). (G) Schematic representation of L1 and L2: indices for spatial scale of auxin maxima pattern in numerical simulations. ai (or xi) and (or ) are auxin (or X) concentrations in cell i and apoplast (i, j), respectively. pi,j is PIN1 density of the membrane toward cell j in cell i.