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

Abstract

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.

A design principle for floral organ number and arrangement in flowers with bilateral symmetry

“…phytohormone auxin (Bowman et al, 2002;Wang and Jiao, 2018). This idea is similar to the inhibitory field theory that pre-existing organs regulate the initiation position of new organs, as this theory is widely accepted to explain phyllotaxis (Hofmeister, 1868;Snow, 1952, 1962;Adler et al, 1997;Dourdy and Couder, 1996a,b;Traas, 2013;Refahi et al, 2016;Kuhlemeier, 2017;Yonekura et al, 2019). Therefore, the inhibitory field may be key for understanding bilaterally symmetric floral organ arrangements.…”

A sense of place, many times over ‐ pattern formation and evolution of repetitive morphological structures

“…For example, inhibitory fields of leaf primordia have been proposed to affect spacing during phyllotactic patterning, and already Turing himself, and others, have argued that activator‐inhibitor pairs might underlie the patterning phenomenon of phyllotaxis . How exactly such interplay of positional information and self‐organizing principles is realized, however, and in which way the rate of apical‐basal growth as determined by the SAM affects this balance, is an area of active investigation using both theoretical and experimental approaches …”

“…Once progenitors leave the PFR, cell fate decision into either joint-or cartilage-forming cells instruct the digit segmentation pattern into individual "phalanges," potentially modulated by BMP inhibitors released from previously formed elements determined by the SAM affects this balance, is an area of active investigation using both theoretical and experimental approaches. 62,67,77…”

Molecular and Hormonal Regulation of Leaf Morphogenesis in Arabidopsis

“…The development and maintenance of SAM are crucial for determining the spatiotemporal arrangement (e.g., clockwise, anticlockwise, spiral and whorled) of aerial organs around the stem. The process of arranging different organs spatially is known as phyllotaxis, which is species and stage-dependent [ 9 , 10 , 11 ].…”