Auxin-driven patterning with unidirectional fluxes

Mikolaj Cieslak, Adam Runions, Przemyslaw Prusinkiewicz

Abstract

The plant hormone auxin plays an essential role in the patterning of plant structures. Biological hypotheses supported by computational models suggest that auxin may fulfil this role by regulating its own transport, but the plausibility of previously proposed models has been questioned. We applied the notion of unidirectional fluxes and the formalism of Petri nets to show that the key modes of auxin-driven patterning - the formation of convergence points and the formation of canals - can be implemented by biochemically plausible networks, with the fluxes measured by dedicated tally molecules or by efflux and influx carriers themselves. Common elements of these networks include a positive feedback of auxin efflux on the allocation of membrane-bound auxin efflux carriers (PIN proteins), and a modulation of this allocation by auxin in the extracellular space. Auxin concentration in the extracellular space is the only information exchanged by the cells. Canalization patterns are produced when auxin efflux and influx act antagonistically: an increase in auxin influx or concentration in the extracellular space decreases the abundance of efflux carriers in the adjacent segment of the membrane. In contrast, convergence points emerge in networks in which auxin efflux and influx act synergistically. A change in a single reaction rate may result in a dynamic switch between these modes, suggesting plausible molecular implementations of coordinated patterning of organ initials and vascular strands predicted by the dual polarization theory.

Reference

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• Video S1: Canalization using Mitchison's model implemented with tally molecules (MP4, 0.23 Mb)
• Video S2: Canalization using Mitchison's model with tally molecules and extracellular space (MP4, 0.33 Mb)
• Video S3: Canalization using a variant of Mitchison's model with tally molecules and extracellular space, in which PIN allocation is controlled by the ratio of unidirectional fluxes instead of the net flux (MP4, 1.2 Mb)
• Video S4: Canalization with exocytosis controlled by one tally molecule. The model is defined by the Petri net in Fig. 6a (MP4, 0.36 Mb)
• Video S5: Canalization with exocytosis controlled by two tally molecules. The model is defined by the Petri net in Fig. 6c MP4, (0.35 Mb)
• Video S6: Convergence point formation with exocytosis controlled by tally molecules (MP4, 0.45 Mb)
• Video S7: Dual-polarization with exocytosis controlled by tally molecules (MP4, 0.2 Mb)
• Video S8: Canalization with exocytosis controlled by influx and efflux carriers bound to auxin in the membrane (MP4, 0.22 Mb)
• Video S9: Convergence point formation with exocytosis controlled by influx and efflux carriers bound to auxin in the membrane (MP4, 0.25 Mb)
• Video S10: Dual polarization with exocytosis controlled by influx and efflux carriers bound to auxin in the membrane (MP4, 0.26 Mb)
• Video S11: Canalization with exocytosis controlled by influx and efflux carriers that act via a mediating molecule (MP4, 0.31 Mb)
• Video S12: Convergence point formation with exocytosis controlled by influx and efflux carriers that act via a mediating molecule (MP4, 0.37 Mb)
• Video S13: Canalization with endocytosis controlled by influx and efflux carriers that act via a mediating molecule (MP4, 0.44 Mb)
• Video S14: Convergence point formation with endocytosis controlled by influx and efflux carriers that act via a mediating molecule (MP4, 0.82 Mb)
• Video S15: Dynamics of pattern formation in a file of cells, with PIN polarized by auxin efflux and influx acting antagonistically (MP4, 0.25 Mb)
• Video S16: Dynamics of pattern formation in a file of cells, with PIN polarized by auxin efflux and influx acting synergistically (MP4, 0.2 Mb)

Video for the HFSP web note: Convergence point and vein formation - switch between synergistic and antagonistic modes controlled by auxin concentration (MP4, 0.2 Mb)