title: Auxin-driven patterning with unidirectional fluxes.
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.
authors.affiliation: Department of Computer Science, University of Calgary, 2500 University Dr. N.W., Calgary, AB T2N 1N4, Canada.
authors.forename: Mikolaj
authors.initials: M
authors.lastname: Cieslak
authors.affiliation: Department of Computer Science, University of Calgary, 2500 University Dr. N.W., Calgary, AB T2N 1N4, Canada.
authors.forename: Adam
authors.initials: A
authors.lastname: Runions
authors.affiliation: Department of Computer Science, University of Calgary, 2500 University Dr. N.W., Calgary, AB T2N 1N4, Canada pwp@cpsc.ucalgary.ca.
authors.forename: Przemyslaw
authors.initials: P
authors.lastname: Prusinkiewicz
mesh_terms: D017360:Arabidopsis / Q000254:growth & development* / Q000378:metabolism; D029681:Arabidopsis Proteins / Q000235:genetics* / Q000378:metabolism; D001692:Biological Transport; D007210:Indoleacetic Acids / Q000378:metabolism*; D008954:Models, Biological; D010937:Plant Growth Regulators / Q000378:metabolism*; D015398:Signal Transduction
chemical_list: D029681:Arabidopsis Proteins; D007210:Indoleacetic Acids; D010937:Plant Growth Regulators
keywords: Petri nets; auxin-driven patterning; canalization; convergence point formation; dual polarization; modulated feedback; polar auxin transport; unidirectional flux.