The REPLUMLESS Transcription Factor Controls the Expression of the RECEPTOR-LIKE CYTOPLASMIC KINASE VI_A2 Gene Involved in Shoot and Fruit Patterning of Arabidopsis thaliana.

The promoter of the RECEPTOR-LIKE CYTOPLASMIC KINASE VI_A2 (RLCK VI_A2) gene contains nine binding sites for the REPLUMLESS (RPL) transcription factor. In agreement, the expression of the kinase gene was strongly downregulated in the rpl-4 mutant. Comparing phenotypes of loss-of-function mutants, it was revealed that both genes are involved in stem growth, phyllotaxis, organization of the vascular tissues, and the replum, highlighting potential functional interactions. The expression of the RLCKVI_A2 gene from the constitutive 35S promoter could not complement the rpl-4 phenotypes but exhibited a dominant positive effect on stem growth and affected vascular differentiation and organization. The results also indicated that the number of vascular bundles is regulated independently from stem thickness. Although our study cannot demonstrate a direct link between the RPL and RLVKVI_A2 genes, it highlights the significance of the proper developmental regulation of the RLCKVI_A2 promoter for balanced stem development.

Evolutionary origins of Fibonacci phyllotaxis in land plants.

Fibonacci phyllotaxis is commonly seen in all major groups of land plants. While a precise correlation is found between the internal pattern of the primary vascular system and the external pattern of appendages on the stem surface, it remains a big question how this regularity of Fibonacci phyllotaxis came into being in the course of evolution. Here I address this problem with a model describing phylogenetic and ontogenetic changes in vascular phyllotaxis based on two hypotheses. The first is that the Fibonacci pattern of vascular connection is uniquely determined by the primary arrangement of incipient primordia, the sources of the primary signal system in vascular tissue differentiation. The second is that the surface-area-to-volume ratio of primary vascular tissues serves as a measure of fitness in evolution. The model explains the empirical rule on the manner in which vascular connection is reconfigured during ontogeny, especially during juvenile development. Fossil and phylogenetic evidence suggests that Fibonacci phyllotaxis appeared shortly after the innovation of indefinite lateral organ initiation in a regular sequence.

The hidden diversity of vascular patterns in flower heads.

Vascular systems are intimately related to the shape and spatial arrangement of the plant organs they support. We investigate the largely unexplored association between spiral phyllotaxis and the vascular system in Asteraceae flower heads. We imaged heads of eight species using synchrotron-based X-ray micro-computed tomography and applied original virtual reality and haptic software to explore head vasculature in three dimensions. We then constructed a computational model to infer a plausible patterning mechanism. The vascular system in the head of the model plant Gerbera hybrida is qualitatively different from those of Bellis perennis and Helianthus annuus, characterized previously. Cirsium vulgare, Craspedia globosa, Echinacea purpurea, Echinops bannaticus, and Tanacetum vulgare represent variants of the Bellis and Helianthus systems. In each species, the layout of the main strands is stereotypical, but details vary. The observed vascular patterns can be generated by a common computational model with different parameter values. In spite of the observed differences of vascular systems in heads, they may be produced by a conserved mechanism. The diversity and irregularities of vasculature stand in contrast with the relative uniformity and regularity of phyllotactic patterns, confirming that phyllotaxis in heads is not driven by the vasculature.

Enigmatic fossil plants with three-dimensional, arborescent-growth architecture from the earliest Carboniferous of New Brunswick, Canada.

The evolution of arborescence in Devonian plants, followed by their architectural radiation in the Carboniferous, is a transition fundamental to Earth-system processes and ecological development. However, this evolutionary transition in trees is based on preserved trunks, of which only a few known specimens possess crowns. We describe Mississippian-aged (Tournaisian) trees with a unique three-dimensional crown morphology from New Brunswick, Canada. The trees were preserved by earthquake-induced, catastrophic burial of lake-margin vegetation. The tree architecture consists of an unbranched, 16-cm-diameter trunk with compound leaves arranged in spirals of ∼13 and compressed into ∼14 cm of vertical trunk length. Compound leaves in the upper ∼0.75 m of the trunk measure >1.75 m in length and preserve alternately arranged secondary laterals beginning at 0.5 m from the trunk; the area below the trunk bears only persistent leaf bases. The principal specimen lacks either apical or basal sections, although an apex is preserved in another. Apically, the leaves become less relaxed toward horizontal and are borne straight at an acute angle at the crown. The compact leaf organization and leaf length created a crown volume of >20-30 m3. This growth strategy likely maximized light interception and reduced resource competition from groundcover. From their growth morphology, canopy size, and volume, we propose that these fossils represent the earliest evidence of arborescent subcanopy-tiering. Moreover, although systematically unresolved, this specimen shows that Early Carboniferous vegetation was more complex than realized, signaling that it was a time of experimental, possibly transitional and varied, growth architectures.

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.

Size-correlated polymorphisms in phyllotaxis-like periodic and symmetric tentacle arrangements in hydrozoan Coryne uchidai.

Introduction: Periodic organ arrangements occur during growth and development and are widespread in animals and plants. In bilaterian animals, repetitive organs can be interpreted as being periodically arranged along the two-dimensional space and defined by two body axes; on the other hand, in radially symmetrical animals and plants, organs are arranged in the three-dimensional space around the body axis and around plant stems, respectively. The principles of periodic organ arrangement have primarily been investigated in bilaterians; however, studies on this phenomenon in radially symmetrical animals are scarce. Methods: In the present study, we combined live imaging, quantitative analysis, and mathematical modeling to elucidate periodic organ arrangement in a radially symmetrical animal, Coryne uchidai (Cnidaria, Hydrozoa). Results: The polyps of C. uchidai simultaneously formed multiple tentacles to establish a regularly angled, ring-like arrangement with radial symmetry. Multiple rings periodically appeared throughout the body and mostly maintained symmetry. Furthermore, we observed polymorphisms in symmetry type, including tri-, tetra-, and pentaradial symmetries, as individual variations. Notably, the types of radial symmetry were positively correlated with polyp diameter, with a larger diameter in pentaradial polyps than in tetra- and triradial ones. Our mathematical model suggested the selection of size-correlated radial symmetry based on the activation-inhibition and positional information from the mouth of tentacle initiation. Discussion: Our established quantification methods and mathematical model for tentacle arrangements are applicable to other radially symmetrical animals, and will reveal the widespread association between size-correlated symmetry and periodic arrangement principles.

Towards solving the mystery of spiral phyllotaxis.

The mystery of the morphogenesis of phyllotaxis has been of concern for several generations of botanists and mathematicians. Of particular interest is the fact that the number of visible spirals is equal to the number from the Fibonacci series. The article proposes an analytical solution to two fundamental questions of phyllotaxis: what is the morphogenesis of patterns of spiral phyllotaxis? and why the number of visible spirals is equal to number from the Fibonacci series? The article contains videos illustrating the recursive dynamic model of spiral phyllotaxis morphogenesis.

High-resolution, respiratory-resolved coronary MRA using a Phyllotaxis-reordered variable-density 3D cones trajectory.

PURPOSE: To develop a respiratory-resolved motion-compensation method for free-breathing, high-resolution coronary magnetic resonance angiography (CMRA) using a 3D cones trajectory. METHODS: To achieve respiratory-resolved 0.98 mm resolution images in a clinically relevant scan time, we undersample the imaging data with a variable-density 3D cones trajectory. For retrospective motion compensation, translational estimates from 3D image-based navigators (3D iNAVs) are used to bin the imaging data into four phases from end-expiration to end-inspiration. To ensure pseudo-random undersampling within each respiratory phase, we devise a phyllotaxis readout ordering scheme mindful of eddy current artifacts in steady state free precession imaging. Following binning, residual 3D translational motion within each phase is computed using the 3D iNAVs and corrected for in the imaging data. The noise-like aliasing characteristic of the combined phyllotaxis and cones sampling pattern is leveraged in a compressed sensing reconstruction with spatial and temporal regularization to reduce aliasing in each of the respiratory phases. RESULTS: In initial studies of six subjects, respiratory motion compensation using the proposed method yields improved image quality compared to non-respiratory-resolved approaches with no motion correction and with 3D translational correction. Qualitative assessment by two cardiologists and quantitative evaluation with the image edge profile acutance metric indicate the superior sharpness of coronary segments reconstructed with the proposed method (P < 0.01). CONCLUSION: We have demonstrated a new method for free-breathing, high-resolution CMRA based on a variable-density 3D cones trajectory with modified phyllotaxis ordering and respiratory-resolved motion compensation with 3D iNAVs.

Modeling phyllotaxis: From the inhibition potential to the real plant.

We developed a new parametrization of the classic Douady and Couder model of phyllotaxis based on the inhibition potential: it allowed us to accurately reproduce the vegetative meristem of Linum usitatissimum displaying Fibonacci phyllotaxis, and the reproductive meristem of Ranunculus repens. We calculated the inhibition potential within the meristem and the auxin concentration at the front. We show that phyllotaxis modes and the convergence of the divergence angles towards "noble" angles are the consequence of minimizing the inhibitory potential under the constraint of decreasing plastochron ratios. Our approach, which gives a physicochemical basis to the van Iterson diagram, produces the same results as approaches based on mechanical constraints, suggesting these are two facets of the same botanical reality.

Phyllotaxis transition over the lifespan of a palm tree using Magnetic Resonance Imaging (MRI) and Terrestrial Laser Scanning (TLS): the case of Jubaea chilensis.

BACKGROUND: Jubaea chilensis (Molina) Baillon, is a uniquely large palm species endemic to Chile. It is under threatened status despite its use as an ornamental species throughout the world. This research seeks to identify the phyllotaxis of the species based on an original combination of non-destructive data acquisition technologies, namely Magnetic Resonance Imaging (MRI) in saplings and young individuals and Terrestrial Laser Scanning (TLS) in standing specimens, and a novel analysis methodology. RESULTS: Two phyllotaxis parameters, parastichy pairs and divergence angle, were determined by analyzing specimens at different developmental stages. Spiral phyllotaxis patterns of J. chilensis progressed in complexity from parastichy pairs (3,2) and (3,5) in juvenile specimens and (5,3), (8,5) and (8,13) for adult specimens. Divergence angle was invariable and averaged 136.9°, close to the golden angle. Phyllotactic pattern changes associated with establishment phase, the adult vegetative and the adult reproductive phases were observed. Both technologies, MRI and TLS proved to be adequate for the proposed analysis. CONCLUSIONS: Understanding phyllotactic transitions may assist identification of developmental stages of wild J. chilensis specimens. The proposed methodology may also be useful for the study of other palm species.

Leaf morphogenesis: The multifaceted roles of mechanics.

Plants produce a rich diversity of biological forms, and the diversity of leaves is especially notable. Mechanisms of leaf morphogenesis have been studied in the past two decades, with a growing focus on the interactive roles of mechanics in recent years. Growth of plant organs involves feedback by mechanical stress: growth induces stress, and stress affects growth and morphogenesis. Although much attention has been given to potential stress-sensing mechanisms and cellular responses, the mechanical principles guiding morphogenesis have not been well understood. Here we synthesize the overarching roles of mechanics and mechanical stress in multilevel and multiple stages of leaf morphogenesis, encompassing leaf primordium initiation, phyllotaxis and venation patterning, and the establishment of complex mature leaf shapes. Moreover, the roles of mechanics at multiscale levels, from subcellular cytoskeletal molecules to single cells to tissues at the organ scale, are articulated. By highlighting the role of mechanical buckling in the formation of three-dimensional leaf shapes, this review integrates the perspectives of mechanics and biology to provide broader insights into the mechanobiology of leaf morphogenesis.

Prophyll in Monocots: The Starting Point of Lateral Shoot Phyllotaxis.

In monocots, the prophyll (or flower bracteole) is the first leaf of the lateral shoot. Typically, the prophyll occurs in an adaxial position toward the main axis; it bears two teeth at its apex and often two keels on the dorsal side. Some authors have hypothesized that the prophyll appeared in evolution as a result of the fusion of two phyllomes. However, in different monocot taxa, prophyll morphology results from the mechanical pressure of the surrounding organs and it cannot be regarded as two fused leaves. In Commelinaceae, if the lateral shoot develops extravaginally (i.e., penetrates the sheath) and the prophyll is not under pressure, the apical teeth and keels are missing. If the lateral shoot starts development intravaginally and under moderate pressure, the prophyll exhibits keels and a bidentate shape. In the bulbs of Amaryllidaceae, which are under strong pressure, the teeth of the prophyll become more pronounced, and the prophyll is dissected into two distinct lobes. In some monocots, the evolutionary trend leads to complete prophyll reduction. Investigations of lateral shoot phyllotaxis have found that the positions of all the subsequent phyllomes of the lateral shoot are sensitive to the prophyll position; they become rearranged if the prophyll deviates from the standard adaxial location (e.g., becoming oblique or transversal). As a generalization in Amaryllidaceae, I have proposed the axiomatic "phantom" method for modeling the prophyll position and shoot branching in cases of complete prophyll reduction. Using the phantom method, I reinvestigated the structure of sympodial units in Philodendron (Araceae). Previous interpretation of the two-keeled cataphyll as a prophyll appeared to be erroneous. In a new interpretation of the sympodial unit, the prophyll and the subsequent leaf are reduced and the cataphyll is the third leaf in the leaf series. A comparative morphological study in Araceae has revealed that prophylls of vegetative shoots rarely elongate and resemble round scales with obscure boundaries with the main axis. This observation could explain prophyll reduction in Philodendron. As such, the positional control of phyllotaxis by the prophyll may be revealed even when the prophyll is completely reduced.

Sucrose Synthase and Fructokinase Are Required for Proper Meristematic and Vascular Development.

Sucrose synthase (SuSy) and fructokinase (FRK) work together to control carbohydrate flux in sink tissues. SuSy cleaves sucrose into fructose and UDP-glucose; whereas FRK phosphorylates fructose. Previous results have shown that suppression of the SUS1,3&4 genes by SUS-RNAi alters auxin transport in the shoot apical meristems of tomato plants and affects cotyledons and leaf structure; whereas antisense suppression of FRK2 affects vascular development. To explore the joint developmental roles of SuSy and FRK, we crossed SUS-RNAi plants with FRK2-antisense plants to create double-mutant plants. The double-mutant plants exhibited novel phenotypes that were absent from the parent lines. About a third of the plants showed arrested shoot apical meristem around the transition to flowering and developed ectopic meristems. Use of the auxin reporter DR5::VENUS revealed a significantly reduced auxin response in the shoot apical meristems of the double-mutant, indicating that auxin levels were low. Altered inflorescence phyllotaxis and significant disorientation of vascular tissues were also observed. In addition, the fruits and the seeds of the double-mutant plants were very small and the seeds had very low germination rates. These results show that SUS1,3&4 and FRK2 enzymes are jointly essential for proper meristematic and vascular development, and for fruit and seed development.

Phyllotaxis without symmetry: what can we learn from flower heads?

Phyllotaxis is commonly considered in the context of circular meristems or receptacles, yet non-circular (fasciated) structures also give rise to new primordia and organs. Here we investigate phyllotactic patterns in fasciated flower heads in the Asteraceae plant family. We begin by surveying the phenomenon of fasciation. We then show that phyllotactic patterns in fasciated heads can be generated by removing the inessential assumption of circularity from the previously published model of gerbera heads. To characterize these patterns, we revisit the conceptual framework in which phyllotactic patterns are commonly described. We note that some notions, in particular parastichies and parastichy numbers, maintain their significance in non-circular phyllotaxis, whereas others, in particular the divergence angle, need to be extended or lose their role. These observations highlight a number of open problems related to phyllotaxis in general, which may be elucidated by studies of fasciated heads.

Fibonacci spirals may not need the Golden Angle.

Phyllotaxis, the regular arrangement of plant lateral organs, is an important aspect of quantitative plant biology. Some models relying on the geometric relationship of the shoot apex and organ primordia focus mainly on spiral phyllotaxis, a common phyllotaxis mode. While these models often predict the dependency of Fibonacci spirals on the Golden Angle, other models do not emphasise such a relation. Phyllotactic patterning in Asteraceae is one such example. Recently, it was revealed that auxin dynamics and the expansion and contraction of the active ring of the capitulum (head) are the key processes to guide Fibonacci spirals in gerbera (Gerbera hybrida). In this Insights paper, we discuss the importance of auxin dynamics, distinct phases of phyllotactic patterning, and the transition of phyllotaxis modes. These findings signify the local interaction among primordia in phyllotactic patterning and the notion that Fibonacci spirals may not need the Golden Angle.

Aperiodic crystals in biology.

Biological systems display a broad palette of hierarchically ordered designs spanning over many orders of magnitude in size. Remarkably enough, periodic order, which profusely shows up in non-living ordered compounds, plays a quite subsidiary role in most biological structures, which can be appropriately described in terms of the more general aperiodic crystal notion instead. In this topical review I shall illustrate this issue by considering several representative examples, including botanical phyllotaxis, the geometry of cell patterns in tissues, the morphology of sea urchins, or the symmetry principles underlying virus architectures. In doing so, we will realize that albeit the currently adopted quasicrystal notion is not general enough to properly account for the rich structural features one usually finds in biological arrangements of matter, several mathematical tools and fundamental notions belonging to the aperiodic crystals science toolkit can provide a useful modeling framework to this end.

Phyllotaxis development: a lesson from the Asteraceae family.

Phyllotaxis refers to the spatial arrangement of leaves and flowers on a stem. A recent study by Zhang et al. described the developmental process underlying phyllotaxis establishment in the capitulum of Gerbera hybrida. This work represents a cornerstone for studying the development and diversification mechanisms of capitula in the Asteraceae.

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.

Rotation angle of stem cell division plane controls spiral phyllotaxis in mosses.

The spiral arrangement (phyllotaxis) of leaves is a shared morphology in land plants, and exhibits diversity constrained to the Fibonacci sequence. Phyllotaxis in vascular plants is produced at a multicellular meristem, whereas bryophyte phyllotaxis emerges from a single apical stem cell (AC) that is embedded in a growing tip of the gametophyte. An AC is asymmetrically divided into itself and a single 'merophyte', producing a future leaf and a portion of the stem. Although it has been suggested that the arrangement of merophytes is regulated by a rotation of the division plane of an AC, the quantitative description of the merophyte arrangement and its regulatory mechanism remain unclear. To clarify them, we examined three moss species, Tetraphis pellucida, Physcomitrium patens, and Niphotrichum japonicum, which exhibit 1/3, 2/5, and 3/8 spiral phyllotaxis, respectively. We measured the angle between the centroids of adjacent merophytes relative to the AC centroid on cross-transverse sections. At the outer merophytes, this divergence angle converged to nearly 120[Formula: see text] in T. pellucida, 136[Formula: see text] in N. japonicum, and 141[Formula: see text] in P. patens, which was nearly consistent with phyllotaxis, whereas the divergence angle deviated from the converged angle at the inner merophytes near an AC. A mathematical model, which assumes scaling growth of AC and merophytes and a constant angle of division plane rotation, quantitatively reproduced the sequence of the divergence angles. This model showed that successive relocations of the centroid position of an AC upon its division inevitably result in the transient deviation of the divergence angle. As a result, the converged divergence angle was equal to the rotation angle, predicting that the latter is a major regulator of the spiral phyllotaxis diversity in mosses.