A plausible model of phyllotaxis

Abstract

A striking phenomenon unique to the kingdom of plants is the regular arrangement of lateral organs around a central axis, known as phyllotaxis. Recent molecular-genetic experiments indicate that active transport of the plant hormone auxin is the key process regulating phyllotaxis. A conceptual model based on these experiments, introduced by Reinhardt et al. [Reinhardt, D., Pesce, E. R., Stieger, P., Mandel, T., Baltensperger, K., et al. (2003) Nature 426, 255-260], provides an intuitively plausible interpretation of the data, but raises questions of whether the proposed mechanism is, in fact, capable of producing the observed temporal and spatial patterns, is robust, can start de novo, and can account for phyllotactic transitions, such as the frequently observed transition from decussate to spiral phyllotaxis. To answer these questions, we created a computer simulation model based on data described previously or in this paper and reasonable hypotheses. The model reproduces, within the standard error, the divergence angles measured in Arabidopsis seedlings and the effects of selected experimental manipulations. It also reproduces distichous, decussate, and tricussate patterns. The model thus offers a plausible link between molecular mechanisms of morphogenesis and the geometry of phyllotaxis.

Fig. 1.

Conceptual model of the regulation of phyllotaxis by polar auxin fluxes in the shoot meristem. Adapted from ref. . (A) PIN1 orientation directs auxin fluxes (arrows) in the L1 layer, leading to accumulation of auxin (red color) at the initiation site (I1) in the peripheral zone. This accumulation eventually results in organ induction. (B) Later, basipetal PIN1 polarization inside the bulging primordium (P1) drains auxin into inner layers, depleting the neighboring L1 cells. As a consequence, another auxin maximum is created in the peripheral zone at position I1 removed from primordia P1 and P2.

Fig. 2.

DR5::GFP expression in the shoot apex. (A) Longitudinal section of a DR5::GFP-expressing wild-type inflorescence meristem. The arrowhead indicates local overexpression of DR5::GFP consistent with an initial. (B) Longitudinal section of a DR5::GFP-expressing wild-type inflorescence meristem treated with 25 μM sirtinol during 48 h. (C, D, F, and G) Transverse confocal pictures, taken with comparable settings. (C) DR5::GFP expression pattern in a pin1-7 inflorescence meristem. (D) DR5::GFP expression pattern in a wildtype inflorescence meristem treated with 20 μM NPA during 24 h. (E) Top view of a wild-type inflorescence meristem, visualized with a binocular microscope. (F) Transverse confocal picture showing the DR5::GFP expression pattern in the same meristem as shown in the frame indicated in E. Spots of GFP signal are observed in the peripheral zone of the meristem where no bulge is visible (compare to E). (G) DR5::GFP expression pattern in a wild-type inflorescence meristem treated with 25 μM sirtinol during 48 h. (H) Longitudinal view of the two first, 3-day-old, leaf primordia of a DR5::GFP-expressing seedling. Note the strong signals at the tips of the primordia (arrowheads), and DR5::GFP expression in the future midveins (arrows), which connect with the stem vasculature (asterisk). P indicates the DR5::GFP expression in the next primordium. (Scale bars: 25 μm.)

Fig. 3.

Pattern generation by the transport-based model. (A–D) Pattern emergence in a sequence of 50 cells with wraparound boundary conditions (the leftmost and the rightmost cell are considered neighbors). Taller bars (brighter green) indicate higher IAA concentration. Simulation steps 30, 60, 70, and 80 are shown. A small amount of noise present in the initial distribution is required to break symmetry. (E and F) Pattern dependence on model parameters. Model parameters affect how many peaks a given number of cells will create. Higher values of the transport coefficient result in more peaks. If the transport coefficient is too low, no peaks will form at all. Transport coefficient: A-D, 4.0; E, 3.0; F, 10.0. (G) Pattern formed in a simulated cellular structure. PIN1 is depicted in red.

Fig. 4.

Simulated shoot apical meristems. (A–D) The arrangement of primordia into phyllotactic patterns: distichous (A), decussate (B), tricussate (C), and spiral (D). (E–G) Simulated pin1 mutant (E), primordium formed in the pin1 mutant after localized application of auxin in the peripheral zone (F), and primordium ring formed in the pin1 mutant after localized application of auxin at the tip of the apex (G). Arrows indicate the site of auxin application. (H and I) Simulated results of cell ablation: control apex (H) and the apex in which five cells shown in black have been removed (I). Note the shift in the position of the primordium initial (cells with high auxin concentration, shown in bright green) near the ablation site.

Fig. 5.

Comparison of the divergence angles: angles measured in Arabidopsis with standard error bars (blue), and angles generated by the spiral phyllotaxis model (red).