Phyllotaxis: Cooperation and competition between mechanical and biochemical processes

Newell, Alan C.; Shipman, Patrick D.; Sun, Zhi-Wei

doi:10.1016/j.jtbi.2007.11.036

Cited by 95 publications

(101 citation statements)

References 41 publications

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“…The molecular view mostly has included growth and an inhibition from earlier primordia where for example reaction-diffusion mechanisms have been proposed [Chapman and Perry, 1987, 2 A c c e p t e d m a n u s c r i p t Meinhardt, 1982]. Recently, also combinations of molecular and mechanical mechanisms have been investigated in a continuous model [Newell et al, 2007].…”

Section: Introductionmentioning

confidence: 99%

Regulated transport as a mechanism for pattern generation: Capabilities for phyllotaxis and beyond

Sahlin

Söderberg

Jönsson

2009

Journal of Theoretical Biology

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Section: Introductionmentioning

confidence: 99%

Regulated transport as a mechanism for pattern generation: Capabilities for phyllotaxis and beyond

Sahlin

Söderberg

Jönsson

2009

Journal of Theoretical Biology

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“…The radial wavenumbers are continuous. Earlier analyses [9], using near-onset amplitude expansions, identified the fixed points corresponding to these shapes but did not prove that the pattern in an annulus at one radius evolves smoothly to that in its neighbor. The PDE simulation does.…”

Section: Resultsmentioning

confidence: 93%

“…Mechanistic explanations, the "hows" rather than the "whys," are given in the works of Green, by Meyerowitz, Traas, Kuhlemeier and Reinhardt, and by Newell, Shipman and colleagues. They have focused on pattern forming physical and biochemical mechanisms: the buckling of the plant's tunica [7], the triggering of auxin inhomogenetities by PIN1 protein transport in cells [8] near its shoot apical meristem (SAM) or combinations thereof [9].…”

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confidence: 99%

Phyllotaxis, Pushed Pattern-Forming Fronts, and Optimal Packing

Pennybacker

Newell

2013

Phys. Rev. Lett.

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We demonstrate that the pattern forming partial differential equation derived from the auxin distribution model proposed by Meyerowitz, Traas and others gives rise to all spiral phyllotaxis properties observed on plants. We show how the advancing pushed pattern front chooses spiral families enumerated by Fibonacci sequences with all attendant self similar properties, a new amplitude invariant curve and connect the results with the optimal packing based algorithms previously used to explain phyllotaxis. Our results allow us to make experimentally testable predictions.

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“…The labels C, F, K, and M are provided to clarify the discussion in Sect. 2 Swarup et al 2005), vein formation (Feugier et al 2005;Feugier and Iwasa 2006;Merks et al 2007;Mitchison 1980a;Mitchison et al 1981;Rolland-Lagan and Prusinkiewicz 2005) and organ initiation (de Reuille et al 2006;Heisler and Jönsson 2006;Jönsson et al 2006;Laskowski et al 2008;Stoma et al 2008;Newell et al 2008;Perrine-Walker et al 2010;Smith et al 2006;Stoma et al 2008), for example. Early studies (Goldsmith et al 1981;Martin et al 1990;Mitchison 1980b) considered only a single line of cells, with auxin diffusion within the cytoplasms and with passive and carrier-mediated transport across the cell membranes; these showed how the efflux carriers increase the tissue-scale auxin flux.…”

Section: Introductionmentioning

confidence: 99%

“…The benefits of this multiscale analytical approach have recently been highlighted by Twycross et al (2010). Similar modelling approaches have been used to study calcium dynamics (Goel et al 2006), pattern formation (Newell et al 2008) and nutrient distributions (Shipley et al 2009), for example, and the effective tissue-scale auxin transport has also been considered in Chavarría-Krauser and Ptashnyk (2009); Kramer (2002); Martin et al (1990); Mitchison (1980a,b); Mitchison et al (1981) and Newell et al (2008).…”

Section: Introductionmentioning

confidence: 99%

Multiscale modelling of auxin transport in the plant-root elongation zone

Band

King

2011

J. Math. Biol.

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In the root elongation zone of a plant, the hormone auxin moves in a polar manner due to active transport facilitated by spatially distributed influx and efflux carriers present on the cell membranes. To understand how the cell-scale active transport and passive diffusion combine to produce the effective tissue-scale flux, we apply asymptotic methods to a cell-based model of auxin transport to derive systematically a continuum description from the spatially discrete one. Using biologically relevant parameter values, we show how the carriers drive the dominant tissue-scale auxin flux and we predict how the overall auxin dynamics are affected by perturbations to these carriers, for example, in knockout mutants. The analysis shows how the dominant behaviour depends on the cells' lengths, and enables us to assess the relative importance of the diffusive auxin flux through the cell wall. Other distinguished limits are also identified and their potential roles discussed. As well as providing insight into auxin transport, the study illustrates the use of multiscale (cell to tissue) methods in deriving simplified models that retain the essential biology and provide understanding of the underlying dynamics.

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Phyllotaxis: Cooperation and competition between mechanical and biochemical processes

Cited by 95 publications

References 41 publications

Regulated transport as a mechanism for pattern generation: Capabilities for phyllotaxis and beyond

Regulated transport as a mechanism for pattern generation: Capabilities for phyllotaxis and beyond

Phyllotaxis, Pushed Pattern-Forming Fronts, and Optimal Packing

Multiscale modelling of auxin transport in the plant-root elongation zone

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