Finding the center of a phyllotactic pattern

The calculation of divergence angles between primordia in a plant apex depends on the point used as the center of the apex. In mathematically ideal phyllotactic patterns, the center is well defined but there has not been a precise definition for the center of naturally occurring phyllotactic patterns. A few techniques have been proposed for estimating the location of the center but without a precise definition for the center the accuracy of these methods cannot be known. This paper provides a precise definition that can be used as the center of a phyllotactic pattern and a numerical method which can accurately find it. These tools will make it easier to compare theory against experiment in phyllotaxis.     

CAPITULUM PHYLLOTAXIS AND NUMERICAL CANALIZATION IN MICROSERIS PYGMAEA (ASTERACEAE: LACTUCEAE)

The positions at which floret primordia arise in developing capitulum buds of Microseris pygmaea D. Don have been mapped by computer-assisted light microscopy. The primordia can be assigned positions along a basic phyllotactic spiral with a divergence angle of about 137.5°. In addition, there are regular deviations from a spiral arrangement. Typically, the first 26 primordia in phyllotactic sequence are arranged in two concentric circles of 13 primordia with considerable deviations in the divergence angle and in the distances between primordia along a parastichy at positions 13 and 26. This arrangement can be simulated by geometric models that include nearest neighbor packing, together with spiral phyllotaxis. The circular arrangement of peripheral primordia at nearly equal radial distances from the center of the developing capitulum helps to explain the numerical constancy (canalization) of peripheral structures, especially the constant number of 13 inner phyllaries on heads with very different numbers of florets.     

Meristic variation in Potamogeton flowers

Flowers of Potamogeton normally have a completely tetramerous plan. Deviations from this norm occur quite commonly in the uppermost flowers of the inflorescence; these variations have been reported before and usually involve a reduction in number of parts. Cases have now been found where the gynoecium of all or many flowers differs from the normal tetracarpellate arrangement; some species regularly have fewer and others more than four carpels. The developmental bases of meristic variation have been explored and quantitative studies of gynoecia and developing gynoecia have been undertaken. The data are used to evaluate the control and correlation of floral development in Potamogeton in general, and in particular the relationship between the gynoecium and the rest of the flower. The developing flower passes through two successive phases of organ initiation: one in which the perianth and stamen primordia arise, and one in which the gynoecial primordia arise. There seems to be little developmental relationship between the two phases except phyllotactic continuity. During the perianth/stamen phase each stamen primordium arises directly above a perianth member, and the presence of a perianth member seems to be a prerequisite for initiation of the stamen. The perianth/stamen phase seems to be rather stable so that normally four perianth/stamen associations are initiated, except in flowers at the tip of the inflorescence. In the gynoecial phase the number of carpel primordia initiated seems to depend on the relative size of carpel primordia and floral apex, and on whether or not the floral apex continues to grow while initiating carpel primordia.     

PHYLLOTACTIC CHANGE INDUCED BY GIBBERELLIC ACID IN XANTHIUM SHOOT APICES

Gibberellic acid (GA) treatment of vegetative shoots of Xanthium leads to a change in phyllotaxis as diagnosed in transverse sections of apical buds. A method of analysis is proposed for estimating the phyllotactic parameters, the plastochron ratio, a, and the divergence angle, α, from measurements of the angular and radial positions of leaf primordia in sections. GA treatment significantly decreases the plastochron ratio, a, from 1.35 in controls, to 1.19 in GA-treated plants, as shown by an analysis of variance, but has no significant effect on the divergence angle. The estimates of a and α are compared with the parameters of theoretical phyllotaxis models, leading to the designation (2, 3) for controls, and (3, 5) for GA-treated plants, where the integers 2, 3, and 5 designate sets of contact parastichies. The change in a is interpreted as indicating a change in the relative position at which leaf primordia are initiated in the apical meristem, and this effect is discussed in relation to theories of leaf initiation.     

Gibberellin-induced reorganization of spatial relationships of emerging leaf primordia at the shoot apical meristem in Hedera helix L.

The transition from spiral to distichous leaf arrangement during gibberellic-acid (GA₃)-induced rejuvenation in Hedera was studied in detail by scanning electron microscopy of the shoot apical meristem. The transition, which involves the initiation of about 14 new leaf primordia, is accomplished by progressive increments in the divergence angle between the leaf primordia from an initial average value of 138.9 ° until it approaches 180 °. This process is preceded, as well as accompanied, by an increased radial displacement of young leaf primordia away from the apical meristem. Although the width of the leaf primordia also increases, this is unlikely to be a causal factor since it occurs only late in the transition. The size of the primordium-free area of the apical meristem is also unlikely to be involved. Quantitative analysis shows that the divergence angle of consecutive leaf primordia commonly fluctuates between relatively large and small values. Thus the transitional stages form a spirodistichous arrangement in which the divergence angle within each pair of leaves is large relative to that between leaf pairs. The stimulation of the radial displacement of the leaf primordia and the associated phyllotactic transition may involve GA₃-induced modification in the spatial organization of cortical microtubules in the apical meristem and related changes in directional cell expansion.Abbreviations DA divergence angle - GA₃ gibberellic acid We thank Mr. Gilbert Ahlstrand for his advice regarding scanning electron microscopy. This paper is contribution of the University of Minnesota Agricultural Experimental Station No. 18,726.     

CORKSCREW1 defines a novel mechanism of domain specification in the maize shoot

In higher plants, determinate leaf primordia arise in regular patterns on the flanks of the indeterminate shoot apical meristem (SAM). The acquisition of leaf form is then a gradual process, involving the specification and growth of distinct domains within the three leaf axes. The recessive corkscrew1 (cks1) mutation of maize (Zea mays) disrupts both leaf initiation patterns in the SAM and domain specification within the mediolateral and proximodistal leaf axes. Specifically, cks1 mutant leaves exhibit multiple midribs and leaf sheath tissue differentiates in the blade domain. Such perturbations are a common feature of maize mutants that ectopically accumulate KNOTTED1-like homeobox (KNOX) proteins in leaf tissue. Consistent with this observation, at least two knox genes are ectopically expressed in cks1 mutant leaves. However, ectopic KNOX proteins cannot be detected. We therefore propose that CKS1 primarily functions within the SAM to establish boundaries between meristematic and leaf zones. Loss of gene function disrupts boundary formation, impacts phyllotactic patterns, and leads to aspects of indeterminate growth within leaf primordia. Because these perturbations arise independently of ectopic KNOX activity, the cks1 mutation defines a novel component of the developmental machinery that facilitates leaf-versus-shoot development in maize.     

Stem fasciated, a recessive mutation in sunflower (Helianthus annuus), alters plant morphology and auxin level

BACKGROUND AND AIMS: Plant lateral organs such as leaves arise from a group of initial cells within the flanks of the shoot apical meristem (SAM). Alterations in the initiation of lateral organs are often associated with changes in the dimension and arrangement of the SAM as well as with abnormal hormonal homeostasis. A mutation named stem fasciated (stf) that affects various aspects of plant development, including SAM shape and auxin level, was characterized in sunflower (Helianthus annuus). METHODS: F1, F2 and F3 generations were obtained through reciprocal crosses between stf and normal plants. For the genetic analysis, a chi2 test was used. Phenotypic observations were made in field-grown and potted plants. A histological analysis of SAM, hypocotyl, epicotyl, stem and root apical meristem was also conducted. To evaluate the level of endogenous indole-3-acetic acid (IAA), a capillary gas chromatography-mass spectrometry-selected ion monitoring analysis was performed. KEY RESULTS: stf is controlled by a single nuclear recessive gene. stf plants are characterized by a dramatically increased number of leaves and vascular bundles in the stem, as well as by a shortened plastochron and an altered phyllotaxis pattern. By histological analysis, it was demonstrated that the stf phenotype is related to an enlarged vegetative SAM. Microscopy analysis of the mutant's apex also revealed an abnormal enlargement of nuclei in both central and peripheral zones and a disorganized distribution of cells in the L2 layer of the central zone. The stf mutant showed a high endogenous free IAA level, whereas auxin perception appeared normal. CONCLUSIONS: The observed phenotype and the high level of auxin detected in stf plants suggest that the STF gene is necessary for the proper initiation of primordia and for the establishment of a phyllotactic pattern through control of both SAM arrangement and hormonal homeostasis.     

Gain and loss of photosynthetic membranes during plastid differentiation in the shoot apex of Arabidopsis

Chloroplasts of higher plants develop from proplastids, which are undifferentiated plastids that lack photosynthetic (thylakoid) membranes. In flowering plants, the proplastid-chloroplast transition takes place at the shoot apex, which consists of the shoot apical meristem (SAM) and the flanking leaf primordia. It has been believed that the SAM contains only proplastids and that these become chloroplasts only in the primordial leaves. Here, we show that plastids of the SAM are neither homogeneous nor necessarily null. Rather, their developmental state varies with the specific region and/or layer of the SAM in which they are found. Plastids throughout the L1 and L3 layers of the SAM possess fairly developed thylakoid networks. However, many of these plastids eventually lose their thylakoids during leaf maturation. By contrast, plastids at the central, stem cell-harboring region of the L2 layer of the SAM lack thylakoid membranes; these appear only at the periphery, near the leaf primordia. Thus, plastids in the SAM undergo distinct differentiation processes that, depending on their lineage and position, lead to either development or loss of thylakoid membranes. These processes continue along the course of leaf maturation.     

Inflorescence and flower development in the Hedychieae (Zingiberaceae): Hedychium coccineum Smith

The inflorescence of Hedychium coccineum Smith is thyrse, and the primary bracts are initiated in a spiral phyllotactic pattern on the sides of the inflorescence dome. Cincinnus primordia are initiated on the flank of the inflorescence apex, in the axils of primary bracts. This primordium subsequently develops a bract and a floral primordium. Then, the floral primordium enlarges, flattens apically, and becomes rounded. Sepals are initiated sequentially from the rounded corner of the primordium ring sepal initiation, and the floral primordium continues to enlarge and produces a ring primordium. Later, this ring primordium separates three common primordia surrounding a central cavity. The adaxial common primordium is the first separation. This primordium produces the posterior petal and the fertile stamen. The remaining two common primordia separate and produce respectively a petal and a petaloid, the inner androecial member. As the flower enlarges, the cavity of the floral cup becomes a rounded–triangular apex; these apices are the sites of outer androecial primordium initiation. The abaxial outer androecial member slightly forms before the two adaxial members develop. But this primordium ceases growth soon after initiation, while the two posterior primordia continue growth to produce the lateral petaloid staminodes. During this stage, gynoecial initiates in the floral cup and continues to grow until extending beyond the labellum.     

Development and structure of trichotomous branching in Edgeworthia chrysantha (Thymelaeaceae)

We studied the development and structure of the unusual trichotomous branching of Edgeworthia chrysantha. Three "branch primordia" are formed sequentially on the shoot apex of a main axis and develop into trichotomous branching. The branch primordia are clearly distinguishable from the typical axillary buds of other angiosperms; they develop much more rapidly than axillary buds, and the borders between the branch primordia and shoot apex of the main axis are anatomically unclear. Furthermore, at a later stage, leaves subtending the branch primordia produce typical axillary buds. These results suggest that the trichotomous branching in this species involves the division of the shoot apical meristem. Expression analysis of genes involved in branching or maintenance of the shoot apical meristem in this species should clarify the control mechanism of this novel branching pattern in angiosperms. We also observed the phyllotactic patterns in trichotomous branching and have related these patterns to the shoot system as a whole.     

Phyllotaxis in two species ofRubia,R. akane andR. sikkimensis

Phyllotaxis and vascular course in the vegetative shoots ofRubia akane andR. sikkimensis were studied. Each node of both species has a whorl of four leafy members among which two are true leaves. Arrangement of the true leaves is not decussate but bijugate, i.e., opposite leaves are arranged spirally. Bijugy was ascertained not only by gross morphology but also by arrangement of primordia around the shoot apex and vascular course through several internodes. Divergence angle differed widely with internodes even within a single shoot and with shoots even in the internodes which are separated by a same number of nodes from the apex. Mean divergence angles obtained for five youngest internodes of some shoots were between 49.4° and 61.8° inR. akane and between 53.6° and 59.4° inR. sikkimensis. Young seedlings ofR. akane showed decussate phyllotaxis in the lowermost several internodes. In the internodes near the lower end of the bijugate part, the divergence angle was wider than in the upper internodes. The directions of the phyllotactic spirals in the main axis and the lateral branches were either homodromous or antidromous, and those in the oppositely paired branches also were either homo- or antidromous.     

Do Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis?

Complex biological patterns are often governed by simple mathematical rules. A favourite botanical example is the apparent relationship between phyllotaxis (i.e. the arrangements of leaf homologues such as foliage leaves and floral organs on shoot axes) and the intriguing Fibonacci number sequence (1, 2, 3, 5, 8, 13 . . .). It is frequently alleged that leaf primordia adopt Fibonacci-related patterns in response to a universal geometrical imperative for optimal packing that is supposedly inherent in most animate and inanimate structures. This paper reviews the fundamental properties of number sequences, and discusses the under-appreciated limitations of the Fibonacci sequence for describing phyllotactic patterns. The evidence presented here shows that phyllotactic whorls of leaf homologues are not positioned in Fibonacci patterns. Insofar as developmental transitions in spiral phyllotaxis follow discernible Fibonacci formulae, phyllotactic spirals are therefore interpreted as being arranged in genuine Fibonacci patterns. Nonetheless, a simple modelling exercise argues that the most common spiral phyllotaxes do not exhibit optimal packing. Instead, the consensus starting to emerge from different subdisciplines in the phyllotaxis literature supports the alternative perspective that phyllotactic patterns arise from local inhibitory interactions among the existing primordia already positioned at the shoot apex, as opposed to the imposition of a global imperative of optimal packing.  © 2006 The Linnean Society of London, Botanical Journal of the Linnean Society , 2006, 150 , 3–24.     

Geometrical relationships specifying the phyllotactic pattern of aquatic plants

The complete range of various phyllotaxes exemplified in aquatic plants provide an opportunity to characterize the fundamental geometrical relationships operating in leaf patterning. A new polar-coordinate model was used to characterize the correlation between the shapes of shoot meristems and the arrangements of young leaf primordia arising on those meristems. In aquatic plants, the primary geometrical relationship specifying spiral vs. whorled phyllotaxis is primordial position: primordia arising on the apical dome (as defined by displacement angles θ ≤ 90° during maximal phase) are often positioned in spiral patterns, whereas primordia arising on the subtending axis (as defined by displacement angles of θ ≥ 90° during maximal phase) are arranged in whorled patterns. A secondary geometrical relationship derived from the literature shows an inverse correlation between the primordial size?:?available space ratio and the magnitude of the Fibonacci numbers in spiral phyllotaxis or the number of leaves per whorl in whorled phyllotaxis. The data available for terrestrial plants suggest that their phyllotactic patterning may also be specified by these same geometrical relationships. Major exceptions to these correlations are attributable to persistent embryonic patterning, leaflike structures arising from stipules, congenital splitting of young primordia, and/or non-uniform elongating of internodes. The geometrical analysis described in this paper provides the morphological context for interpreting the phenotypes of phyllotaxis mutants and for constructing realistic models of the underlying mechanisms responsible for generating phyllotactic patterns.     

DIFFERENTIATION OF LATERAL SHOOTS AS THORNS IN ULEX EUROPAEUS

Ulex europaeus is a much-branched shrub with small, narrow, spine-tipped leaves and axillary thorn shoots. The origin and development of axillary shoots was studied as a basis for understanding the changes that occur in the axillary shoot apex as it differentiates into a thorn. Axillary bud primordia are derived from detached portions of the apical meristem of the primary shoot. Bud primordia in the axils of juvenile leaves on seedlings develop as leafy shoots while those in the axils of adult leaves become thorns. A variable degree of vegetative development prior to thorn differentiation is exhibited among these secondary thorn shoots even on the same axis. Commonly the meristems of secondary axillary shoots initiate 3–9 bracteal leaves with tertiary axillary buds before differentiating as thorns. In other cases the meristems develop a greater number of leaves and tertiary buds as thorn differentiation is delayed. The initial stages in the differentiation of secondary shoot meristems as thorns are detected between plastochrons 10–20, depending on vigor of the parent shoot. A study of successive lateral buds on a shoot shows an abrupt conversion from vegetative development to thorn differentiation. The conversion involves the termination of meristematic activity of the apex and cessation of leaf initiation. Within the apex a vertical elongation of cells of the rib meristem initials and their immediate derivatives commences the attenuation of the apex which results in the pointed thorn. All cells of the apex elongate parallel to the axis and proceed to sclerify basipetally. Back of the apex some cortical cells in which cell division has persisted longer differentiate as chlorenchyma. Although no new leaves are initiated during the extension of the apex, provascular strands are present in the thorn tip. Fibrovascular bundles and bundles of cortical fibers not associated with vascular tissue differentiate in the thorn tip and are correlated in position with successive incipient leaves in the expected phyllotactic sequence, the more developed bundles being related to the first incipient leaves. Some secondary shoots displayed variable atypical patterns of meristem differentiation such as abrupt conversion of the apex resulting in sclerification with limited cell elongation and small, inhibited leaves. These observations raise questions concerning the nature of thorn induction and the commitment of meristems to thorns.     

Floral development in Astragalus caspicus Bieb. (Leguminosae: Papilionoideae: Galegeae)

Floral organogenesis and development of the bushy perennial legume Astragalus caspicus were studied using epi-illumination light microscopy techniques. Based on our observations, flowers are in axillary two-flowered racemes, initiate all 21 floral organs and show precocious appearance of zygomorphy. The order of floral organ initiation is unidirectional in whorls starting from the abaxial position of the flower with a high degree of overlap. Another important ontogenetic feature is the existence of two successive common primordial stages categorized as primary and secondary. The primary common primordia produce antesepalous stamens and secondary common primordia. In contrast, the five secondary common primordia subdivide into a petal and an antepetalous stamen primordia. Our findings on floral ontogeny of A. caspicus provide new evidence for the complex and variable floral initiation and development in legumes. The floral apex with strong overlapping initiation of different organs illustrates a paradox in which different capabilities must be presumed to exist simultaneously. Moreover, two extraordinary types of common primordia represent possibly an advanced evolutionary trend where time intervals between the initiations of different floral organs in Papilionoideae are shortened.     

Studies of aberrant phyllotaxy1 Mutants of Maize Indicate Complex Interactions between Auxin and Cytokinin Signaling in the Shoot Apical Meristem

One of the most fascinating aspects of plant morphology is the regular geometric arrangement of leaves and flowers, called phyllotaxy. The shoot apical meristem (SAM) determines these patterns, which vary depending on species and developmental stage. Auxin acts as an instructive signal in leaf initiation, and its transport has been implicated in phyllotaxy regulation in Arabidopsis (Arabidopsis thaliana). Altered phyllotactic patterns are observed in a maize (Zea mays) mutant, aberrant phyllotaxy1 (abph1, also known as abphyl1), and ABPH1 encodes a cytokinin-inducible type A response regulator, suggesting that cytokinin signals are also involved in the mechanism by which phyllotactic patterns are established. Therefore, we investigated the interaction between auxin and cytokinin signaling in phyllotaxy. Treatment of maize shoots with a polar auxin transport inhibitor, 1-naphthylphthalamic acid, strongly reduced ABPH1 expression, suggesting that auxin or its polar transport is required for ABPH1 expression. Immunolocalization of the PINFORMED1 (PIN1) polar auxin transporter revealed that PIN1 expression marks leaf primordia in maize, similarly to Arabidopsis. Interestingly, maize PIN1 expression at the incipient leaf primordium was greatly reduced in abph1 mutants. Consistently, auxin levels were reduced in abph1, and the maize PIN1 homolog was induced not only by auxin but also by cytokinin treatments. Our results indicate distinct roles for ABPH1 as a negative regulator of SAM size and a positive regulator of PIN1 expression. These studies highlight a complex interaction between auxin and cytokinin signaling in the specification of phyllotactic patterns and suggest an alternative model for the generation of altered phyllotactic patterns in abph1 mutants. We propose that reduced auxin levels and PIN1 expression in abph1 mutant SAMs delay leaf initiation, contributing to the enlarged SAM and altered phyllotaxy of these mutants.     

Orthostichy, Parastichy and Plastochrone Ratio in a Central Theory of Phyllotaxis

A view of phyllotaxis theory is proposed which combines theessentials of the orthostichy, parastichy and plastochrone ratioideas. The advocated thesis takes cognisance of the biologicallyexact tangential divergence angles between nodes or primordiaand this is in contrast with other major theories which haveassumed the attainment of mathematically ‘ideal’divergence angles. Rectiserial orthostichy lines are demonstratedto be present in both 'spiral' and ‘non-spiral’systems. Basically similar mathematical laws govern the definitionof such systems whether the phyllotaxis designation be Fibonacci,anomalous or multijugate. The inter-relationships of the variousangular and other measures associated with plastochrone ratio,orthostichy lines and parastichy curves are dealt with in detail.     

Inflorescence and Flower Development of Globba barthei ( Zingiberaceae)

Inflorescence of Globba barthei is a thyrse . Primary bracts are initiated in a spiral phyllotactic pattern on the inflorescence apex . Cincinnus primordia are initiated in the axils of primary bracts . These promordia develop secondarybracts and floral primordia . The floral primordium continues to enlarge and produce a ring primordium . Sepals are initiated sequentially from the rounded corner of the primordium . The ring primordium separates three common primordium surrounding a central cavity . The adaxial common primordium is the first to separate . This primordium divides transversely and producespetal and fertile stamen . The remaining two common primordium transversely separate and produce respectively a petal and a petaloid . As the flower developing , the cavity of the floral cup becomes triangular . The angles of this triangle are the sites of outer androecial primordium . The abaxial androecia forms slightly earlier than the two adaxial ones, and then this primordium ceases growth soon . The two posterior primordia continue growth to produce the lateral petaloid staminodes . During this stage , gynoecia initiate from the floral cup and continue to fuse and develop into style and stigma. In addition ,Initiation of the bulbil primordium is observed at base of inflorescence axis during the early floral development . The bulbil primordium initiates in the axil of primary bract . The evolutionary significance of six androecia is discussed .