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

Abstract

The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulators 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, thus 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.

Polar auxin transport: models and mechanisms

“…Consequently, cell polarisation in these models requires perturbations that push the system beyond these unstable equilibria into the realm of the polar equilibria. We find that in those models (Feugier and Iwasa, 2006;Feugier et al, 2005;Fujita and Mochizuki, 2006;Alim and Frey, 2010), in which a finite PIN pool is assumed, no bipolar equilibrium with high PIN levels at both membranes is present. By contrast, in the early models by Mitchison (Mitchison, 1980;Mitchison, 1981) and in the model by Stoma et al (Stoma et al, 2008) (which is based on these early models) no limiting PIN pool is incorporated and a bipolar state does occur, resulting in more possibilities for nonpolar cells.…”

“…In addition to the model by Stoma et al (Stoma et al, 2008) that we used as an example, we analysed a variety of published fluxbased models (Mitchison, 1980;Mitchison, 1981;Feugier and Iwasa, 2006;Feugier et al, 2005;Fujita and Mochizuki, 2006;Alim and Frey, 2010). Summarising, we find that all flux-based models, independent of the shape of the feedback function, auxin pumping dynamics or whether a limiting PIN pool is assumed, are capable of generating polarity-driven self-organised auxin and PIN patterns.…”

“…The auxin transport capacity is represented by membrane permeability in early models (Mitchison, 1980;Mitchison, 1981) and by membrane PIN concentration in later models (e.g. Fujita and Mochizuki, 2006;Feugier and Iwasa, 2006;Alim and Frey, 2010;Feugier et al, 2005;Stoma et al, 2008). Flux-based models have mainly been used to model venation patterns, and demonstrate that small fluctuations in auxin may be amplified into more distinct streams, with PINs pointing in the direction of the flux, i.e.…”

Noise and Robustness in Phyllotaxis

“…We studied the continuous limit of these cellular models as in [48], [57]; the details are presented in the Text S1.…”

Modelling the emergence of polarity patterns for the intercellular transport of auxin in plants

“…As a consequence, the presence of an auxin gradient becomes a necessary condition for PIN polarization. Here, we consider instead dynamics based on flux sensing where PIN recycling rates are modulated by the amount of auxin flux transported by those same PIN transporters [30,31]. Mathematically, we take the PIN dynamics on a face f ( f ¼ N, S, E, W ) of a cell to be specified by a Hill equation of exponent h:…”