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.