An auxin-driven polarized transport model for phyllotaxis

Abstract

Recent studies show that plant organ positioning may be mediated by localized concentrations of the plant hormone auxin. Auxin patterning in the shoot apical meristem is in turn brought about by the subcellular polar distribution of the putative auxin efflux mediator, PIN1. However, the question of what signals determine PIN1 polarization and how this gives rise to regular patterns of auxin concentration remains unknown. Here we address these questions by using mathematical modeling combined with confocal imaging. We propose a model that is based on the assumption that auxin influences the polarization of its own efflux within the meristem epidermis. We show that such a model is sufficient to create regular spatial patterns of auxin concentration on systems with static and dynamic cellular connectivities, the latter governed by a mechanical model. We also optimize parameter values for the PIN1 dynamics by using a detailed auxin transport model, for which parameter values are taken from experimental estimates, together with a template consisting of cell and wall compartments as well as PIN1 concentrations quantitatively extracted from confocal data. The model shows how polarized transport can drive the formation of regular patterns.Arabidopsis thaliana ͉ computable plant ͉ dynamical model ͉ pattern formation ͉ meristem I n the growing plant shoot, new leaf and flower primordia emerge at well defined positions, resulting in strikingly regular patterns (1). These phyllotactic patterns can be whorled (more than one new primordium develops simultaneously) or spiral (single primordia are created sequentially). Spiral phyllotaxis is often connected to the Fibonacci series because the numbers of parastichies (visible spirals) in each direction around the axis are commonly consecutive Fibonacci numbers. Also, consecutive primordia in the spiral often appear at a divergence angle close to the golden angle. The beautiful symmetries apparent in phyllotaxis and its connection to mathematics have inspired scientists to create theories and models to explain these patterns. One important finding from mathematical analysis and physical simulation (2, 3) is that many of the seemingly complex phyllotactic patterns and transitions found in plants can probably be explained to a large degree by any regular spacing mechanism superimposed on a gradually enlarging generative region. This finding is important because it suggests that the problem can be reduced to two potentially independent and smaller questions. The first question regards how meristem size is determined during plant development. The second question involves how a regularly spaced pattern of primordial position is specified. Traditionally, models have concentrated on the second question, and they can be divided into molecular and mechanical ideas (4-6). Because we investigate a model based on molecular experiments, here we discuss some molecular-based ideas in more detail. Schoute (7) first proposed the idea of lateral inhibition based on a diffusible chemical produced b...

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

“…Many computational cell-scale models are being developed to investigate auxin transport (de Reuille et al 2006;Feugier and Iwasa 2006;Feugier et al 2005;Grieneisen et al 2007;Heisler and Jönsson 2006;Jönsson et al 2006;Kramer 2004Kramer , 2009Laskowski et al 2008;Merks et al 2007;Mironova et al 2010;Perrine-Walker et al 2010;Rolland-Lagan and Prusinkiewicz 2005;Smith et al 2006;Stoma et al 2008;Swarup et al 2005); however, little has been done to determine the corresponding tissue-scale descriptions. In this paper, we demonstrate the potential of using (analytical) multiscale methods to simplify an auxin-transport model and to identify the combinations of cell-scale processes that govern the tissue-scale auxin flux.…”

“…Delbarre et al (1996Delbarre et al ( , 1994) measured the passive-diffusion membrane permeability in tobacco cells as 0.14 − 0.18 cm h −1 and the majority of previous modelling studies use estimates around these values (Chavarrıa-Krauser et al 2005;Goldsmith et al 1981;Heisler and Jönsson 2006;Jönsson et al 2006;Kramer 2004Kramer , 2009Swarup et al 2005); thus following Swarup et al (2005), we set P I AAH = 0.2 cm h −1 = 0.56 µm s −1 . Experimental values for the membrane permeabilities due to the influx and efflux carriers have not been well characterised.…”

“…The majority of previous models use the same value for the permeability due to the influx carriers, and therefore we set P AU X 1 = 0.2 cm h −1 = 0.56 µm s −1 Kramer 2004;Swarup et al 2005). In contrast, various values are used for the permeability due to the efflux carriers, including 0.124 µm s −1 (Goldsmith et al 1981;Jönsson et al 2006), 0.27 µm s −1 ), 1.4 µm s −1 (Kramer 2004) and 20 µm s −1 (Laskowski et al 2008). Swarup et al (2005) assume that all the epidermal cells (and similarly all the cortical cells and all the endodermal cells) have an efflux-carrier number proportional to the area of the cell membrane, which, as the efflux carriers are present only on the shootward face of the membrane, results in the efflux-carrier density on this face increasing with cell length.…”

“…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.…”

“…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. More recent studies have considered more complex tissue geometries and have incorporated apoplastic diffusion Jönsson et al 2006;Kramer 2004;Laskowski et al 2008;Swarup et al 2005), saturable carrier-mediated transport (de Reuille et al 2006;Feugier et al 2005;Jönsson et al 2006;Merks et al 2007;Smith et al 2006), cytoplasmic structure (Kramer 2004;Perrine-Walker et al 2010), cell growth (Chavarrıa-Krauser et al 2005;Grieneisen et al 2007;Jönsson et al 2006;Mironova et al 2010;Stoma et al 2008), auxin production and degradation (Feugier and Iwasa 2006;Feugier et al 2005;Perrine-Walker et al 2010;Heisler and Jönsson 2006;Jönsson et al 2006;Smith et al 2006;Stoma et al 2008) and dynamics of the efflux carriers Jönsson et al 2006;Kramer 2009;Merks et al 2007;Mironova et al 2010;Stoma et al 2008).…”