Inhibition fields for phyllotactic pattern formation: a simulation study

Most theories of phyllotaxis are based on the idea that the formation of new primordia is inhibited by the proximity of older primordia. Several mechanisms that could result in such an inhibition have been proposed, including mechanical interactions, diffusion of a chemical inhibitor, and signaling by actively transported substances. Despite the apparent diversity of these mechanisms, their pattern-generation properties can be captured in a unified manner by inhibition fields surrounding the existing primordia. In this paper, we introduce a class of fields that depend on both the spatial distribution and the age of previously formed primordia. Using current techniques to create geometrically realistic, growing apex surfaces, we show that such fields can robustly generate a wide range of spiral, multijugate, and whorled phyllotactic patterns and their transitions. The mathematical form of the inhibition fields suggests research directions for future studies of phyllotactic patterning mechanisms.

[1]  W. Hofmèister.  Allgemeine Morphologie der Gewächse , 1868 .

[2]  S. Schwendener.  Mechanische Theorie der Blattstellungen , 1878 .

[3]  M. Snow,et al.  Experiments on Phyllotaxis. I. The Effect of Isolating a Primordium , 1932 .

[4]  Oscar W. Richards,et al.  The Analysis of the Relative Growth Gradients and Changing Form of Growing Organisms: Illustrated by the Tobacco Leaf , 1943, The American Naturalist.

[5]  C. Wardlaw.  Morphogenesis in Plants , 1953 .

[6]  T. Steeves,et al.  Patterns in plant development: Subject index , 1972 .

[7]  A. Lindenmayer,et al.  PHYLLOTAXIS IN BRYOPHYLLUM TUBIFLORUM: MORPHOGENETIC STUDIES AND COMPUTER SIMULATIONS , 1974 .

[8]  I. Adler.  A model of contact pressure in phyllotaxis. , 1974, Journal of theoretical biology.

[9]  J. Thornley.  Phyllotaxis. I. A Mechanistic Model , 1975 .

[10]  A. Lindenmayer,et al.  Diffusion mechanism for phyllotaxis: theoretical physico-chemical and computer study. , 1977, Plant physiology.

[11]  G. Mitchison,et al.  Phyllotaxis and the Fibonacci Series , 1977, Science.

[12]  D. A. Young,et al.  On the diffusion theory of phyllotaxis. , 1978, Journal of theoretical biology.

[13]  H. Meinhardt.  Models of biological pattern formation , 1982 .

[14]  J. N. Ridley.  Packing efficiency in sunflower heads , 1982 .

[15]  Zygmunt Hejnowicz,et al.  Growth tensor of plant organs , 1984 .

[16]  W. W. Schwabe,et al.  Phyllotaxis: a simple computer model based on the theory of a polarly-translocated inhibitor , 1984 .

[17]  B. Zagórska-Marek.  Phyllotactic patterns and transitions in Abies balsamea , 1985 .

[18]  A. M. Turing,et al.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[19]  Douady,et al.  Phyllotaxis as a physical self-organized growth process. , 1992, Physical review letters.

[20]  P. Green.  Pattern Formation in Shoots: A Likely Role for Minimal Energy Configurations of the Tunica , 1992, International Journal of Plant Sciences.

[21]  Akira Yotsumoto.  A diffusion model for phyllotaxis , 1993 .

[22]  R. V. Jean,et al.  Phyllotaxis: A Systemic Study in Plant Morphogenesis , 1995 .

[23]  Roger V. Jean,et al.  Phyllotaxis: Subject index , 1994 .

[24]  V. Leitáo,et al.  Computer Graphics: Principles and Practice , 1995 .

[25]  E. Coen,et al.  Control of flower development and phyllotaxy by meristem identity genes in antirrhinum. , 1995, The Plant Cell.

[26]  Y. Couder,et al.  Phyllotaxis as a Dynamical Self Organizing Process Part III: The Simulation of the Transient Regimes of Ontogeny , 1996 .

[27]  Y. Couder,et al.  PHYLLOTAXIS AS A DYNAMICAL SELF ORGANIZING PROCESS. PART I: THE SPIRAL MODES RESULTING FROM TIME-PERIODIC ITERATIONS , 1996 .

[28]  R. V. Jean,et al.  A History of the Study of Phyllotaxis , 1997 .

[29]  R. F. Lyndon.  The shoot apical meristem , 1998 .

[30]  Jerzy Nakielski.  TENSORIAL MODEL FOR GROWTH AND CELL DIVISION IN THE SHOOT APEX , 2000 .

[31]  R. V. Jean,et al.  Application of Two Mathematical Models to the Araceae, a Family of Plants with Enigmatic Phyllotaxis , 2001 .

[32]  M. Bennett,et al.  Regulation of phyllotaxis by polar auxin transport , 2003, Nature.

[33]  H. Meinhardt.  Complex pattern formation by a self-destabilization of established patterns: chemotactic orientation and phyllotaxis as examples. , 2003, Comptes rendus biologies.

[34]  Colin Smith,et al.  Local Specification of Surface Subdivision Algorithms , 2003, AGTIVE.

[35]  M. Frenz,et al.  Microsurgical and laser ablation analysis of leaf positioning and dorsoventral patterning in tomato , 2004, Development.

[36]  E. Mjolsness,et al.  An auxin-driven polarized transport model for phyllotaxis , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[37]  O. Deussen,et al.  Contact pressure models for spiral phyllotaxis and their computer simulation. , 2006, Journal of theoretical biology.

[38]  P. Prusinkiewicz,et al.  A plausible model of phyllotaxis , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[39]  D. Kwiatkowska.  Flower primordium formation at the Arabidopsis shoot apex: quantitative analysis of surface geometry and growth. , 2006, Journal of experimental botany.

[40]  B. Zagórska-Marek,et al.  Virtual phyllotaxis and real plant model cases. , 2008, Functional plant biology : FPB.