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SWARTHMORE PHYS 120 - A plausible model of phyllotaxis

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A plausible model of phyllotaxisRichard S. Smith*†, Soazig Guyomarc’h†‡, Therese Mandel‡, Didier Reinhardt‡§, Cris Kuhlemeier‡,and Przemyslaw Prusinkiewicz*¶*Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4; and‡Institute of Plant Sciences,University of Berne, CH-3013 Berne, SwitzerlandCommunicated by Enrico Sandro Coen, John Innes Centre, Norwich, United Kingdom, December 6, 2005 (received for review October 22, 2005)A striking phenomenon unique to the kingdom of plants is theregular arrangement of lateral organs around a central axis, knownas phyllotaxis. Recent molecular-genetic experiments indicate thatactive transport of the plant hormone auxin is the key processregulating phyllotaxis. A conceptual model based on these exper-iments, 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 thedata, but raises questions of whether the proposed mechanism is,in fact, capable of producing the observed temporal and spatialpatterns, is robust, can start de novo, and can account for phyllo-tactic transitions, such as the frequently observed transition fromdecussate to spiral phyllotaxis. To answer these questions, wecreated a computer simulation model based on data describedpreviously or in this paper and reasonable hypotheses. The modelreproduces, within the standard error, the divergence anglesmeasured in Arabidopsis seedlings and the effects of selectedexperimental manipulations. It also reproduces distichous, de-cussate, and tricussate patterns. The model thus offers a plausiblelink between molecular mechanisms of morphogenesis and thegeometry of phyllotaxis.active transport 兩 auxin 兩 PIN 兩 polarity 兩 computer simulationWithin the variety of phyllotactic patterns found in nature, themost intriguing and, at the same time, the most prevalent isthe spiral phyllotactic pattern characterized by the arrangement oforgans into conspicuous spirals (parastichies), where the numbersof parastichies are consecutive elements of the Fibonacci series.This pattern is related to the divergence angle between organsapproximating the golden angle of 137.5°. In the entire world ofdevelopmental biology, phyllotaxis is perhaps the most strikingexample of a phenomenon that can only be described by usingquantitative notions of geometry.The regularity and mathematical properties of spiral phyllotaxishave attracted the attention of biologists and mathematicians sincethe early 19th century. They proposed conceptual, mathematical,and computational models, which elucidated the geometric prop-erties of spiral phyllotactic arrangements (1) and the emergence ofphyllotactic patterns during plant development. This latter categoryof models was pioneered by Hofmeister (2) and Snow and Snow (3),who hypothesized that the creation of new primordia is inhibited bythe proximity of older primordia. New primordia, therefore, can beformed only at a certain minimal distance from the old ones. Thisgeneral hypothesis has subsequently been refined into a number ofcomputational models, postulating and exploring different types ofinhibitory mechanisms such as geometric spacing (4), physicalforces (5, 6), and chemical signals (7, 8).In the absence of molecular data, the proposed mechanisms weremore or less abstract. Recent experiments, however, provided aninsight into the molecular processes involved in phyllotaxis, pointingto the central role of active transport of the plant hormone auxin.When shoot apices were cultivated in the presence of auxintransport inhibitors, the induction of lateral organs was blocked,and the apices grew vigorously as radially symmetric structures.Application of the natural auxin indole-3-acetic acid (IAA) to suchpin-shaped meristems induced lateral primordia, with the size andposition depending on the concentration and the position of theapplied auxin (9). Furthermore, the cellular distribution and sub-cellular localization of the auxin efflux facilitator PIN1 was con-sistent with a role in organ positioning (10).On the basis of these data, Reinhardt et al. (10) proposed aconceptual model of phyllotaxis (ref. 10; Fig. 1). According to thismodel, auxin is transported acropetally toward the meristem, whereit is redirected to the primordia, which function as sinks. As a result,auxin is depleted from the surroundings of the primordia andreaches the organogenetic peripheral zone only at a certain minimaldistance from the two youngest primordia (P1 and P2). Auxinaccumulates at this position, where it induces a new primordium(incipient primordium I1) that, in the course of the plastochron,grows out and becomes a sink itself. The phyllotactic pattern thusresults from the dynamics of interaction between existing andincipient primordia in a growing apex, mediated by the activelytransported auxin.The mechanism proposed by Reinhardt et al. (10) is plausible inthe sense that it is consistent with the available molecular data andcaptures qualitatively the inhibitory effect of the existing primordiaon an incipient primordium. However, the question of whether it isindeed capable of generating the highly constrained geometry ofspiral phyllotactic patterns was open. We answer this question byconstructing a simulation model. It is based on data concerning theinduction of primordia by high auxin concentrations and the polarlocalization of the auxin transport facilitator PIN1 in the surfacelayer of the apex (10). We also include previously undescribedexperimental data focused on the distribution of auxin in themeristem and the incipient primordia. The ensuing model showsthat the molecular mechanisms identified by Reinhardt et al. (10)and further developed in this paper can lead to the formation of thephyllotactic patterns observed in nature.Experimental ResultsPreviously published data in refs. 9–12 formed the initial experi-mental basis for the model. To meet the needs of model construc-tion, we also acquired additional data, focused on the localizationof auxin within the meristem and the incipient primordia.Data Set 1: Phyllotactic Patterning Occurs in the Outer Layer of theShoot Meristem (L)1. The PIN1 protein is located primarily, althoughnot exclusively, in the external L1 layer (figure 1 A and C in ref. 10).This localization suggests that phyllotactic patterns may be formedessentially on the


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