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.

In-Depth Quantification of Cell Division and Elongation Dynamics at the Tip of Growing Arabidopsis Roots Using 4D Microscopy, AI-Assisted Image Processing and Data Sonification.

One of the fundamental questions in plant developmental biology is how cell proliferation and cell expansion coordinately determine organ growth and morphology. An amenable system to address this question is the Arabidopsis root tip, where cell proliferation and elongation occur in spatially separated domains, and cell morphologies can easily be observed using a confocal microscope. While past studies revealed numerous elements of root growth regulation including gene regulatory networks, hormone transport and signaling, cell mechanics and environmental perception, how cells divide and elongate under possible constraints from cell lineages and neighboring cell files has not been analyzed quantitatively. This is mainly due to the technical difficulties in capturing cell division and elongation dynamics at the tip of growing roots, as well as an extremely labor-intensive task of tracing the lineages of frequently dividing cells. Here, we developed a motion-tracking confocal microscope and an Artificial Intelligence (AI)-assisted image-processing pipeline that enables semi-automated quantification of cell division and elongation dynamics at the tip of vertically growing Arabidopsis roots. We also implemented a data sonification tool that facilitates human recognition of cell division synchrony. Using these tools, we revealed previously unnoted lineage-constrained dynamics of cell division and elongation, and their contribution to the root zonation boundaries.

Symmetry and its transition in phyllotaxis.

Symmetry is an important component of geometric beauty and regularity in both natural and cultural scenes. Plants also display various geometric patterns with some kinds of symmetry, of which the most notable example is the arrangement of leaves around the stem, i.e., phyllotaxis. In phyllotaxis, reflection symmetry, rotation symmetry, translation symmetry, corkscrew symmetry, and/or glide reflection symmetry can be seen. These phyllotactic symmetries can be dealt with the group theory. In this review, we introduce classification of phyllotactic symmetries according to the group theory and enumerate all types of phyllotaxis, not only major ones such as spiral and decussate but also minor ones such as orixate and semi-decussate, with their symmetry groups. Next, based on the mathematical model studies of phyllotactic pattern formation, we discuss transitions between phyllotaxis types different in the symmetry class with a focus on the transition into one of the least symmetric phyllotaxis, orixate, as a representative of the symmetry-breaking process. By changes of parameters of the mathematical model, the phyllotactic pattern generated can suddenly switch its symmetry class, which is not constrained by the group-subgroup relationship of symmetry. The symmetry-breaking path to orixate phyllotaxis is also accompanied by dynamic changes of the symmetry class. The viewpoint of symmetry brings a better understanding of the variety of phyllotaxis and its transition.

Mathematical model studies of the comprehensive generation of major and minor phyllotactic patterns in plants with a predominant focus on orixate phyllotaxis.

Plant leaves are arranged around the stem in a beautiful geometry that is called phyllotaxis. In the majority of plants, phyllotaxis exhibits a distichous, Fibonacci spiral, decussate, or tricussate pattern. To explain the regularity and limited variety of phyllotactic patterns, many theoretical models have been proposed, mostly based on the notion that a repulsive interaction between leaf primordia determines the position of primordium initiation. Among them, particularly notable are the two models of Douady and Couder (alternate-specific form, DC1; more generalized form, DC2), the key assumptions of which are that each leaf primordium emits a constant power that inhibits new primordium formation and that this inhibitory effect decreases with distance. It was previously demonstrated by computer simulations that any major type of phyllotaxis can occur as a self-organizing stable pattern in the framework of DC models. However, several phyllotactic types remain unaddressed. An interesting example is orixate phyllotaxis, which has a tetrastichous alternate pattern with periodic repetition of a sequence of different divergence angles: 180°, 90°, -180°, and -90°. Although the term orixate phyllotaxis was derived from Orixa japonica, this type is observed in several distant taxa, suggesting that it may reflect some aspects of a common mechanism of phyllotactic patterning. Here we examined DC models regarding the ability to produce orixate phyllotaxis and found that model expansion via the introduction of primordial age-dependent changes of the inhibitory power is absolutely necessary for the establishment of orixate phyllotaxis. The orixate patterns generated by the expanded version of DC2 (EDC2) were shown to share morphological details with real orixate phyllotaxis. Furthermore, the simulation results obtained using EDC2 fitted better the natural distribution of phyllotactic patterns than did those obtained using the previous models. Our findings imply that changing the inhibitory power is generally an important component of the phyllotactic patterning mechanism.