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Article Addendum

Phyllotaxis as an example of the symbiosis of mechanical forces and biochemical processes in living tissue

Alan C. Newell, Patrick D. Shipman and Zhiying Sun

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Phyllotaxis, the arrangement of a plant's phylla (flowers, bracts, stickers) near its shoot apical meristem (SAM), has intrigued natural scientists for centuries. Even today, the reasons for the observed patterns and their special properties, the physical and chemical mechanisms which give rise to strikingly similar configurations in a wide variety of plants, the almost-constant golden divergence angle, the almost constant plastichrone ratio, the choices of parastichy numbers and the prevalence of Fibonacci sequences to which their numbers belong, are at best only partially understood. Our goals in this Addendum are: i) To give a brief overview of current thinking on possible mechanisms for primordia (the bumps on the plant surface which eventually mature into fully developed structures such as leaves or florets) formation and give a descriptive narrative of the mathematical models which encode various hypotheses. ii) To emphasize the point that patterns, whether they be phyllotactic configurations on plant surfaces or convection cells on the sun's surface, are macroscopic objects whose behaviors are determined more by symmetries of the proposed model and less by microscopic details. Because of this, the identification of observations with the predications of a particular model can only be made with confidence when the match coincides over a range of circumstances and parameters. iii) To discuss some of the key results of the proposed models and, in particular, introduce the prediction of a new and, in principle, measurable invariant in plant phyllotaxis. iv) To introduce a new model of primordia formation which is more in keeping with the pictures and paradigms of Hofmeister,1 Snow & Snow,2 and Douady and Couder3,4 which see primordia as forming in a fairly narrow annular zone surrounding the plant's SAM separating a region of undifferentiated cells from a fully developed patterned state. v) To consider the challenge of phyllotaxis in the broader context of pattern formation in biological tissue which responds to both mechanical and biochemical processes.

Addendum to: Newell AC, Shipman P, Sun Z. Phyllotaxis: Cooperation and competition between biomechnical and biochemical processes. J Theor Biol 2008; 251:421-39.

Authors

Alan C. Newell

Department of Mathematics and Program in Applied Mathematics; University of Arizona

Patrick D. Shipman

Department of Mathematics; University of Maryland-College Park

Zhiying Sun

Program in Applied Mathematics; University of Arizona

Purchase article for $19

Subscribe to this journal for $79/year