A plausible model of auxin-driven patterning in plant development

The feedback between the transport of the plant hormone auxin and the polarization of its transporters plays an essential role in the regulation of plant development. We propose biochemical networks that may implement this feedback in nature.

HFSP Program Grant holder Przemyslaw Prusinkiewicz and colleagues
authored on Tue, 20 October 2015

Auxin controls an astonishing diversity of developmental processes in plants, including the layout of plant organs around their supporting axes (phyllotaxis), the activation of buds, the patterning of vasculature and, the focus of our HFSP grant, the definition of leaf shapes.  It is known that auxin is transported in a polar manner between cells in a tissue, and a family of auxin efflux carriers – PIN proteins – plays an essential role in this transport. Furthermore, computational models have shown that the emergence of auxin-driven patterns regulating plant development can be explained by assuming a feedback between the distribution of auxin and the localization of PIN within cell membranes.  The molecular mechanism of this feedback remains unknown. In our recent work [1], we propose biochemically plausible networks that could implement it in nature.

Figure: Computational model of auxin-driven patterning in a longitudinal section of a plant apex. Large gray squares represent cells.  Grey rectangles and small squares represent extracellular space. Blue squares and rectangles indicate auxin concentration. Black trapezoids indicate auxin fluxes.  PIN concentration in cell membranes is shown in red.  In the steady state, shown here, PIN in the epidermis (top row) directs auxin flow towards the maximum of auxin concentration (top row, center).  In nature, this maximum determines the position of a new organ, such as a flower, leaf, or entire branch.  From there, auxin is directed into the inner tissues, forming a “canal” that patterns a future vascular strand. In this simulation, auxin was produced at a higher rate in the epidermis then in the inner tissues.  The central cell in the bottom row was an auxin sink.  A switch from synergistic to antagonistic PIN polarization occurred when auxin concentration in a cell exceeded a threshold.  The resulting emergent pattern of PIN polarization, auxin flow and auxin concentration is in agreement with observations.  This agreement also includes PIN polarization in the cells below the epidermis and surrounding the canal. See the video for the corresponding dynamic simulation. 

Previously proposed conceptual and computational models of auxin-driven patterning raise three concerns:

Addressing these concerns, we first noticed that simple biochemical circuits can measure unidirectional fluxes. A unidirectional flux is defined as the rate of substance flow in one direction, ignoring the counter-flow.  We then considered several plausible biochemical networks in which both the auxin efflux and influx influence PIN polarization.  Using computational models we showed that the operation of these networks crucially depends on the role of auxin influx.  If auxin efflux and influx act antagonistically (auxin efflux increases and influx decreases PIN allocation to a membrane segment), PIN becomes polarized in the direction of the net auxin flux. In contrast, if auxin efflux and influx act synergistically (both the efflux and influx increase PIN allocation), PIN becomes predominantly polarized towards the neighboring cell with the highest auxin concentration. The switch between antagonistic and synergistic modes may result from as little as the change of a single reaction rate in the network.  It is thus easily achievable, and can lead to the coordinated action of the synergistic and antagonistic polarization modes, implemented by the same network with different parameters.  Such coordinated action provides the best explanation for some of the most fundamental developmental processes in plants, for example the patterning of new organs with the associated vasculature (see Figure).

Our results open a new perspective in the quest for the molecular mechanisms that polarize PIN in vivo. In particular, they suggest a key role of auxin influx as the polarizing factor.  If empirically confirmed, the general features of PIN polarization by unidirectional fluxes will contribute to the view that many aspects of plant development and form can be reduced to broad principles: the emerging laws of developmental biology.

Reference

[1] Auxin-driven patterning with unidirectional fluxes. M. Cieslak, A. Runions, and P. Prusinkiewicz. Journal of Experimental Botany (2015) 66(16): 5085-5102.

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