Symmetry and its transition in phyllotaxis

A new mathematical model of phyllotaxis to solve the genuine puzzle spiromonostichy

Arrangement of plant leaves around the stem, termed phyllotaxis, exhibits beautiful and mysterious regularities and has been one of the most attractive subjects of biological pattern formation. After the long history of studies on phyllotaxis, it is now widely accepted that the inhibitory effect of existing leaf primordia on new primordium formation determines phyllotactic patterning. However, costoid phyllotaxis unique to Costaceae of Zingiberales, displaying spiromonostichy characterized by a steep spiral with a small divergence angle, seems to disagree with the inhibitory effect-based mechanism and has remained as a "genuine puzzle". We developed a new mathematical model, hypothesizing that each leaf primordium exerts not only the inhibitory effect but also some inductive effect. Computer simulations with the new model successfully generated a spiromonostichous pattern when these two effects met a certain relationship. The obtained spiromonostichy matched the real costoid phyllotaxis observed with Costus megalobractea, particularly for the decrease of the divergence angle associated with the enlargement of the shoot apical meristem. The new model was also shown to be able to produce a one-sided distichous pattern that is seen in phyllotaxis of a few plants of Zingiberales and has never been addressed in the previous model studies. These results implicated inductive as well as inhibitory mechanisms in phyllotactic patterning, at least in Zingiberales.

The Search for Geometrical Parameters That Represent the Dynamic Nature of Phyllotaxis in Plants

The shoot apical meristem (SAM) is the main growth centre that produces lateral organs such as leaves in specific and precise symmetrical patterns. The main goal of this commentary is to explore the link between phyllotactic parameters such as the plastochrone ratio (R) as well as Γ (relationship between the size of the SAM and the size of primordia) and growth processes involved in the expression of symmetrical patterns at the level of the SAM. It is also possible to deduce the values of these parameters from measures of the apical area and the radius of the SAM. A comparative analysis of phyllotactic parameters for three species (Begonia scabrida, Euterpe oleracea, and Anagallis arvensis) for which ‘dynamic’ data are available reveals that empirical and theoretical values of R and Γ can differ, indicating that characters defining these parameters are subject to developmental constraints that in turn determine the boundary conditions for the dynamic manifestation of phyllotactic patterns. One of the main challenges that remains is the ability to consistently and effectively observe the dynamic changes taking place at the SAM (in real time) over an extended period.