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.     

灌木铁线莲（毛茛科）花器官的发生与发育

用扫描电子显微镜（SEM）对铁线莲属（Clematis L.）植物灌木铁线莲(C. fruticosa Turcz.)花的形态发生和发育过程进行了观察。灌木铁线莲花原基形成后,4枚萼片以交互对生的方式首先发生,呈轮状排列。最早的4枚雄蕊原基在4枚萼片交接的位置上近螺旋状发生,此后,随着雄蕊原基的向心发生和数目不断增多,其发生的螺旋状序列逐渐明显。雄蕊原基发生后,在花原基顶端,心皮原基沿着雄蕊原基的发生序列呈螺旋状发生。本文结果支持在原始被子植物花中螺旋状排列和轮状排列同时存在的观点。此外,本文也进一步证实了花萼与苞片的同源性。     

Floral phyllotaxis in basal angiosperms: development and evolution

To date, molecular developmental studies have focused on vegetative rather than floral phyllotaxis because vegetative shoot apices are technically more tractable than floral apices in model plants. In contrast to evolutionary changes in the phyllotaxis of vegetative shoots, however, changes in floral phyllotaxis appear to have played a major role in angiosperm evolution. Consolidation of a whorled floral phyllotaxis in derived groups allowed synorganization of floral organs and further adaptive radiations. In basal angiosperms, floral phyllotaxis is more flexible. To study these phenomena, we need clarification of the complex relations of both spiral and whorled phyllotaxis with divergence angles, plastochrons, spiral versus simultaneous initiation of organs, parastichies, orthostichies, organ series, and whorls. Improved resolution of phylogenetic relationships and increased knowledge of the diversity of floral phyllotaxis will allow us to trace evolutionary changes in floral phyllotaxis in ever more detail. Already, such surveys have confirmed that floral phyllotaxis was unusually labile early in angiosperm evolution. Whether the original floral phyllotaxis in angiosperms was spiral or whorled is equivocal, but it appears that spiral floral phyllotaxis in Magnoliales and Laurales is derived rather than primitive.     

A contact pressure model for semi-decussate and related phyllotaxis

Semi-decussate phyllotaxis, in which leaves arise singly and the divergence angles between successive pairs of leaves alternate between approximately 90° and approximately 180°, is accounted for by a contact pressure model. It is assumed that leaf primordia are initiated at a divergence angle close to the Fibonacci angle of 137·5°, that the primordia move under contact pressure, and that when a primordium first experiences contact pressure all other primordia are fixed. Extensions of the model account for: psuedodecussate phyllotaxis, where the leaves appear to arise in pairs; semi-tricussate and pseudo-tricussate phyllotaxis, where the leaves are arranged in, respectively, dissolved or apparent trimerous whorls; and phyllotaxis of the 1,3 series, where the divergence angle is about 100°. The compatibility of the model with current theories of Fibonacci phyllotaxis is discussed.     

Independence of Organogenesis and Cell Pattern in Developing Angle Shoots of Selaginella martensii

Angle meristems are mounds of meristematic tissue located atdorsal and/or ventral branch points of the dichotomising stemaxes of many species of Selaginella (Lycophyta). The presentstudy examined the development of ventral angle shoots of S.martensii in response to removal of distal shoot apices (decapitation).Scanning electron microscopy of sequential replicas of developingangle meristems and angle shoots revealed that for the firsttwo pseudowhorls of leaf primordia, particular leaves are notattributable to particular merophytes of the angle meristemapical cell. Individual leaf primordia of the first (outer)pseudowhorl often form from more than one merophyte. Neitherthe shape of the angle meristem apical cell nor the directionof segmentation has any effect on the development of the angleshoot. Additionally, the apical cell of the angle meristem doesnot necessarily contribute directly to either of the new shootapices of the developing angle shoot. The first bifurcationof the angle shoot shows a remarkably consistent relationshipto the branching pattern of the parent shoot. The strong branchof the first angle shoot bifurcation typically occurs towardthe weak side branch of the parent shoot. Anatomical studiesshowed that bifurcation of the young angle shoot involved theformation of two new growth centres some distance away fromthe original angle meristem apical cell; new apical cells subsequentlyformed within these. These results provide additional supportfor the view that cell lineage has little or no effect on finalform or structure in plants.Copyright 1994, 1999 Academic Press Selaginella martensii Spring, Lycophyta, angle meristem, apical cell, shoot apical meristem, leaf primordium, branching, dichotomy, morphogenesis, determination, competence, development, mould and cast technique, replica technique, scanning electron microscopy     

Flower Development in Silene: Morphology and Sequence of Initiation of Primordia

The initiation and development of the flower of Silene coeli-rosawas followed by examining apices by scanning electron microscopy.The sepals, stamens and carpets are initiated in a spiral sequence,the direction of the spiral king the opposite of the acropetalhelix of unequal axillary buds at the nodes below the flower.The petals are initiated almost simultaneously and at the sametime as the first few stamens. The change in phyllotaxis fromopposite and decussate in the vegetative shoot to spiral inthe flower occurs with the displacement of the first two sepalsaway from the mid-line of the apex and towards the axillarybud at the node below the flower. The sizes of the sepals andstamens are a function of their age since initiation but thepetals grow more slowly. The Silene flower can be interpretedas a shoot bearing primordia with associated axillary primordia,some of the latter being precocious in their development. Silent weli-rosa, flower initiation, flower development, phyllotaxis, primordia     

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.     

Changes in Apical Growth and Phyllotaxis on Flowering and Reversion in Impatiens balsamina L.

When plants of Impatiens balsamina L were subjected to 5 shortdays and then re-placed in long days, they began to form a terminalflower and then reverted to vegetative growth at this terminalshoot apex The onset of flowering was accompanied by an increasein the rate of initiation of primordia, an increase in the growthrate of the apex, a change in primordium arrangement from spiralto whorled or pseudo-whorled, a lack of internodes, and a reductionm the size at initiation of the primordia and also of the stemfrusta which give rise to nodal and internodal tissues On reversion,parts intermediate between petals and leaves were formed, followedby leaves, although in reverted apices the size at initiationand the arrangement of primordia remained the same as in thefloweing apex The apical growth rate and the rate of primordiuminitiation were less in the reverted apices than in floral apicesbut remained higher than in the original vegetative apex Sincethe changes in apical growth which occur on the transition toflowering are not reversed on reversion, the development oforgans as leaves or petals is not directly related to the growthrate of the apex, or the arrangement, rate of initiation orsize at initiation of primordia Impatiens balsamina L, flower reversion, evocation, phyllotaxis, shoot meristem     

Spiral phyllotaxis underlies constrained variation in <Emphasis Type="Italic">Anemone</Emphasis> (Ranunculaceae) tepal arrangement

Stabilization and variation of floral structures are indispensable for plant reproduction and evolution; however, the developmental mechanism regulating their structural robustness is largely unknown. To investigate this mechanism, we examined positional arrangement (aestivation) of excessively produced perianth organs (tepals) of six- and seven-tepaled (lobed) flowers in six Anemone species (Ranunculaceae). We found that the tepal arrangement that occurred in nature varied intraspecifically between spiral and whorled arrangements. Moreover, among the studied species, variation was commonly limited to three types, including whorls, despite five geometrically possible arrangements in six-tepaled flowers and two types among six possibilities in seven-tepaled flowers. A spiral arrangement, on the other hand, was unique to five-tepaled flowers. A spiral phyllotaxis model with stochasticity on initiating excessive primordia accounted for these limited variations in arrangement in cases when the divergence angle between preexisting primordia was less than 144°. Moreover, interspecific differences in the frequency of the observed arrangements were explained by the change of model parameters that represent meristematic growth and differential organ growth. These findings suggest that the phyllotaxis parameters are responsible for not only intraspecific stability but interspecific difference of floral structure. Decreasing arrangements from six-tepaled to seven-tepaled Anemone flowers demonstrate that the stabilization occurs as development proceeds to increase the component (organ) number, in contrast from the intuition that the variation will be larger due to increasing number of possible states (arrangements).     

Statistical recognition of random and regular phyllotactic patterns

AIMS: A statistical method used in ecology is adapted to characterize the degree of order in phyllotactic systems. SCOPE: The test consists of subdividing a planar projection of the stem apical meristem into 16 sectors and counting the number of primordia appearing in each. By dividing the sum of squared deviations by the mean number of primordia per sector the chi-square (chi2) is obtained. When there are a total number of 20 primordia, if the chi2 is less than 6.26, the phyllotaxis is spiral; if it is between 6.26 and 27.5 the phyllotaxis is random; and if it is greater than 27.5, the phyllotaxis is distichous or whorled (level of significance alpha = 5 %). It is also possible to remove one or more sectors. If there are k sectors, the two critical values delimiting the random zone will be found in a chi2 table for k - 1 degrees of freedom. CONCLUSIONS: The method is applied to the analysis of sho mutants described by Itoh et al. in 2000 (Plant Cell 12: 2161-2174). The results obtained are in agreement with the theoretical analysis showing that a whorled or spiral phyllotactic system may contain a certain number of randomly distributed elements without losing its regular global structure.     

The CUP-SHAPED COTYLEDON2 and 3 genes have a post-meristematic effect on Arabidopsis thaliana phyllotaxis

Background and Aims The arrangement of flowers in inflorescence shoots of Arabidopsis thaliana represents a regular spiral Fibonacci phyllotaxis. However, in the cuc2 cuc3 double mutant, flower pedicels are fused to the inflorescence stem, and phyllotaxis is aberrant in the mature shoot regions. This study examined the causes of this altered development, and in particular whether the mutant phenotype is a consequence of defects at the shoot apex, or whether post-meristematic events are involved.Methods The distribution of flower pedicels and vascular traces was examined in cross-sections of mature shoots; sequential replicas were used to investigate the phyllotaxis and geometry of shoot apices, and growth of the young stem surface. The expression pattern of CUC3 was analysed by examining its promoter activity.Key Results Phyllotaxis irregularity in the cuc2 cuc3 double mutant arises during the post-meristematic phase of shoot development. In particular, growth and cell divisions in nodes of the elongating stem are not restricted in the mutant, resulting in pedicel–stem fusion. On the other hand, phyllotaxis in the mutant shoot apex is nearly as regular as that of the wild type. Vascular phyllotaxis, generated almost simultaneously with the phyllotaxis at the apex, is also much more regular than pedicel phyllotaxis. The most apparent phenotype of the mutant apices is a higher number of contact parastichies. This phenotype is associated with increased meristem size, decreased angular width of primordia and a shorter plastochron. In addition, the appearance of a sharp and deep crease, a characteristic shape of the adaxial primordium boundary, is slightly delayed and reduced in the mutant shoot apices.Conclusions The cuc2 cuc3 double mutant displays irregular phyllotaxis in the mature shoot but not in the shoot apex, thus showing a post-meristematic effect of the mutations on phyllotaxis. The main cause of this effect is the formation of pedicel–stem fusions, leading to an alteration of the axial positioning of flowers. Phyllotaxis based on the position of vascular flower traces suggests an additional mechanism of post-meristematic phyllotaxis alteration. Higher density of flower primordia may be involved in the post-meristematic effect on phyllotaxis, whereas delayed crease formation may be involved in the fusion phenotype. Promoter activity of CUC3 is consistent with its post-meristematic role in phyllotaxis.     

Floral development and floral phyllotaxis in Anaxagorea (Annonaceae)

Background and Aims Anaxagorea is the phylogenetically basalmost genus in the large tropical Annonaceae (custard apple family) of Magnoliales, but its floral structure is unknown in many respects. The aim of this study is to analyse evolutionarily interesting floral features in comparison with other genera of the Annonaceae and the sister family Eupomatiaceae. Methods Live flowers of Anaxagorea crassipetala were examined in the field with vital staining, liquid-fixed material was studied with scanning electron microscopy, and microtome section series were studied with light microscopy. In addition, herbarium material of two other Anaxagorea species was cursorily studied with the dissecting microscope. Key Results Floral phyllotaxis in Anaxagorea is regularly whorled (with complex whorls) as in all other Annonaceae with a low or medium number of floral organs studied so far (in those with numerous stamens and carpels, phyllotaxis becoming irregular in the androecium and gynoecium). The carpels are completely plicate as in almost all other Annonaceae. In these features Anaxagorea differs sharply from the sister family Eupomatiaceae, which has spiral floral phyllotaxis and ascidiate carpels. Flat stamens and the presence of inner staminodes differ from most other Annonaceae and may be plesiomorphic in Anaxagorea. However, the inner staminodes appear to be non-secretory in most Anaxagorea species, which differs from inner staminodes in other families of Magnoliales (Eupomatiaceae, Degeneriacae, Himantandraceae), which are secretory. Conclusions Floral phyllotaxis in Anaxagorea shows that there is no signature of a basal spiral pattern in Annonaceae and that complex whorls are an apomorphy not just for a part of the family but for the family in its entirety, and irregular phyllotaxis is derived. This and the presence of completely plicate carpels in Anaxagorea makes the family homogeneous and distinguishes it from the closest relatives in Magnoliales.     

Photomorphogenesis and phyllotaxis during vegetative growth in Sinapis alba and Xanthium strumarium

Abstract The effect of light on the rate of formation of leaf primordia was investigated at the apex of seedlings of Sinapis alba and Xanthium strumarium. It was found that light accelerates this rate. On the other hand, no significant light effect was found on the angles of divergence of successive leaves during the transition from the almost decussate leaf position of the cotyledons to the helical phyllotaxis of the stem leaves. In fact, light and dark grown plants use the same leaves for the transition from decussate to helical phyllotaxis. Thus, if time is plotted in ‘biological units’ (number of primordia) there is no difference between light and dark grown plants. Using scanning electron microscope techniques it was found that the ‘primordia free apical area’ enlarges during development. The rate of enlargement is accelerated by light. However, if time is expressed in biological units (number of primordia) no difference between light and dark grown plants exists. It is concluded that light accelerates the realization of the apical pattern without interfering with the specification of the pattern. In other words, light accelerates the development of an apex without affecting the temporal and spatial coordination of the events.     

STRUCTURE AND DEVELOPMENT OF THE DIMORPHIC BRANCH SYSTEM OF THEOBROMA CACAO

The vegetative morphology of Theobroma cacao, the cacao tree, was studied in order to provide a foundation for further investigations on the morphogenesis of the cacao dimorphic shoot system. The seedling of cacao has a determinate orthotropic shoot with a (2+3) phyllotaxis. Branch dimorphism is initiated after 1 to 2 years of growth at which time the apical meristem of the orthotropic shoot aborts and a pseudowhorl of plagiotropic branches is initiated from axillary positions in the shoot tip. The plagiotropic branches are characterized by a distichous phyllotaxis and indeterminate growth. Subsequently an axillary bud below the pseudowhorl develops into a new orthotropic shoot. The apical meristem of this shoot eventually aborts and another pseudowhorl is formed. The apical anatomy of the two types of shoots is similar. The developmental potentiality of the orthotropic shoot axillary buds to form one or the other type of shoot was investigated. The phyllotaxis of the axillary buds of the orthotropic shoot is spiral and that of the axillary buds of the plagiotropic branch is distichous. Pruning and apical puncture experiments showed that the axillary buds of a plagiotropic branch, and of an orthotropic seedling shoot which has not yet formed a pseudowhorl, always give rise to the parent type of shoot. However, the axillary buds of an orthotropic shoot which already bears a pseudowhorl give rise to either type of shoot for several nodes below the point of origin of the pseudowhorl. The type of shoot has no influence on the form of branch which develops from an axillary bud grafted to it. This evidence supports the hypothesis that the axillary buds are initiated as one or the other type of shoot, i.e., once initiated they are predestined.     

On the diffusion theory of phyllotaxis

An inhibitor diffusion theory of phyllotaxis is examined in the steady-state approximation for cylindrical shoot apex models. The model calculations give rise naturally to common patterns of spiral phyllotaxis, as well as to higher whorled patterns. The model also predicts commonly observed subpatterns of axillary organs superimposed on primary phyllotaxis patterns. Application of the model to phyllotaxis patterns in other organisms and in flowers is proposed.     

A Dynamical Phyllotaxis Model to Determine Floral Organ Number

How organisms determine particular organ numbers is a fundamental key to the development of precise body structures; however, the developmental mechanisms underlying organ-number determination are unclear. In many eudicot plants, the primordia of sepals and petals (the floral organs) first arise sequentially at the edge of a circular, undifferentiated region called the floral meristem, and later transition into a concentric arrangement called a whorl, which includes four or five organs. The properties controlling the transition to whorls comprising particular numbers of organs is little explored. We propose a development-based model of floral organ-number determination, improving upon earlier models of plant phyllotaxis that assumed two developmental processes: the sequential initiation of primordia in the least crowded space around the meristem and the constant growth of the tip of the stem. By introducing mutual repulsion among primordia into the growth process, we numerically and analytically show that the whorled arrangement emerges spontaneously from the sequential initiation of primordia. Moreover, by allowing the strength of the inhibition exerted by each primordium to decrease as the primordium ages, we show that pentamerous whorls, in which the angular and radial positions of the primordia are consistent with those observed in sepal and petal primordia in Silene coeli-rosa, Caryophyllaceae, become the dominant arrangement. The organ number within the outmost whorl, corresponding to the sepals, takes a value of four or five in a much wider parameter space than that in which it takes a value of six or seven. These results suggest that mutual repulsion among primordia during growth and a temporal decrease in the strength of the inhibition during initiation are required for the development of the tetramerous and pentamerous whorls common in eudicots.     

Bud Structure in Relation to Shoot Morphology and Position on the Vegetative Annual Shoots of Juglans regia L. (Juglandaceae)

The length and basal diameter of all lateral and terminal budsof vegetative annual shoots of 7-year-oldJuglans regia treeswere measured. All buds were dissected and numbers of cataphylls,embryonic leaves and leaf primordia were recorded. Each axillarybud was ranked according to the position of its associated leaffrom the apex to the base of its parent shoot. Bud size andcontent were analysed in relation to bud position and were comparedwith the size and number of leaves of shoots in equivalent positionswhich extended during the following growing season. Length andbasal diameter of axillary buds varied according to their positionon the parent shoot. Terminal buds contained more embryonicleaves than any axillary bud. The number of leaves was smallerfor apical and basal axillary buds than for buds in intermediatepositions on the parent shoot only. All new extended shootswere entirely preformed in the buds that gave rise to them.Lateral shoots were formed in the median part of the parentshoot. These lateral shoots derived from buds which were largerthan both apical and basal ones. Copyright 2001 Annals of BotanyCompany Juglans regia L., Persian walnut tree, branching pattern, preformation, bud content, shoot morphology     

Microsurgical and laser ablation analysis of leaf positioning and dorsoventral patterning in tomato

Leaves are arranged according to regular patterns, a phenomenon referred to as phyllotaxis. Important determinants of phyllotaxis are the divergence angle between successive leaves, and the size of the leaves relative to the shoot axis. Young leaf primordia are thought to provide positional information to the meristem, thereby influencing the positioning of new primordia and hence the divergence angle. On the contrary, the meristem signals to the primordia to establish their dorsoventral polarity, which is a prerequisite for the formation of a leaf blade. These concepts originate from classical microsurgical studies carried out between the 1920s and the 1970s. Even though these techniques have been abandoned in favor of genetic analysis, the resulting insights remain a cornerstone of plant developmental biology. Here, we employ new microsurgical techniques to reassess and extend the classical studies on phyllotaxis and leaf polarity. Previous experiments have indicated that the isolation of an incipient primordium by a tangential incision caused a change of divergence angle between the two subsequent primordia, indicating that pre-existing primordia influence further phyllotaxis. Here, we repeat these experiments and compare them with the results of laser ablation of incipient primordia. Furthermore, we explore to what extent the different pre-existing primordia influence the size and position of new organs, and hence phyllotaxis. We propose that the two youngest primordia (P1 and P2) are sufficient for the approximate positioning of the incipient primordium (I1), and therefore for the perpetuation of the generative spiral, whereas the direct contact neighbours of I1 (P2 and P3) control its delimitation and hence its exact size and position. Finally, we report L1-specific cell ablation experiments suggesting that the meristem L1 layer is essential for the dorsoventral patterning of leaf primordia.     

Developmental study on the inflorescence and flower of Caldesia grandis Samuel (Alismataceae)

The inflorescence and floral development of Caldesia grandis Samuel is reported for the first time in this paper. The basic units of the large cymo‐thyrsus inflorescence are short panicles that are arranged in a pseudowhorl. Each panicle gives rise spirally to three bract primordia also arranged in a pseudowhorl. The branch primordia arise at the axils of the bracts. Each panicle produces spirally three bract primordia with triradiate symmetry (or in a pseudowhorl) and three floral primordia in the axils of the bract primordia. The apex of the panicle becomes a terminal floral primordium after the initiations of lateral bract primordia and floral primordia. Three sepal primordia are initiated approximately in a single whorl from the floral primordium. Three petal primordia are initiated alternate to the sepal primordia, but their subsequent development is much delayed. The first six stamen primordia are initiated as three pairs in a single whorl and each pair appears to be antipetalous as in other genera of the Alismataceae. The stamen primordia of the second whorl are initiated trimerously and opposite to the petals. Usually, 9–12 stamens are initiated in a flower. There is successive transition between the initiation of stamen and carpel primordia. The six first‐initiated carpel primordia rise simultaneously in a whorl and alternate with the trimerous stamens, but the succeeding ones are initiated in irregular spirals, and there are 15–21 carpels developed in a flower. Petals begin to enlarge and expand when anthers of stamens have differentiated microsporangia. Such features do not occur in C. parnassifolia. In the latter, six stamen primordia are initiated in two whorls of three, carpel primordia are initiated in 1–3 whorls, and there is no delay in the development of petals. C. grandis is thus considered more primitive and C. parnassifolia more derived. C. grandis shares more similarities in features of floral development with Alsma, Echinodorus, Luronium and Sagittaria. © 2002 The Linnean Society of London, Botanical Journal of the Linnean Society, 2002, 140 , 39–47.