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.     

Two notions of conspicuity and the classification of phyllotaxis

Invoking cylindrical Bravais lattices, Adler (1974, 1977) proposed a mathematically precise definition for the botanical classification of phyllotaxis. It is based on opposed pairs of parastichy families, that are conspicuous and visible. Jean (1988) generalized this concept to non-opposed pairs of parastichy families. In the present paper it is shown that this generalization implies a notion of conspicuity different from Adler's. This is made obvious by redefining the key terms of the two approaches. Both classifications are well defined. For Adler's, this is shown by presenting a general proof for his conjecture that conspicuous (in the sense of Adler) opposed pairs of parastichy families are visible. There are indications that in applications to models of phyllotaxis (van Iterson model, inhibitor models) their solutions are better characterized by Jean's classification. The differences between Adler's and Jean's classification show up only in very rare cases, so that the practice of pattern determination is only insignificantly touched by the present results. It turns out that the widely used contact parastichy method to determine phyllotactic patterns gives results according to Jean's classification rather than Adler's.     

Observations on the Symmetry of the Shoot in Vicia faba and some Allied Species, and on the Transmission of some Morphogenetic Impulses

Axillary buds occur in unsymmetrical arrangements so that anynode must be either right- or left-handed. The two types occurin roughly equal numbers but are not randomly distributed. Thecondition of any node is determined partly by stimuli transmittedfrom the nodes below. The tissues of the stem can act as a filter,transmitting right- and left-handed stimuli with different degreesof efficiency. Although there are considerable interspecificdifferences in respect of these relationships, it is unlikelythat the actual state of right- or left-handedness of a nodeis subject to any direct genetical control. In this respectthe bud arrangements resemble phyllotactic spirals and differfrom most other right- or left-handed structures occurring inplants.     

RELATIONSHIPS BETWEEN SHOOT GROWTH AND CHANGING PHYLLOTAXY OF RANUNCULUS

Growth of Ranunculus shoots through ontogeny is quantified by techniques utilizing scanning electron microscopy and studies on living plant material. The order of the contact parastichy phyllotaxy in the apical system is related to the relative plastochron rates of growth of the shoot. There is a change in the (2, 3) contact parastichy pattern of vegetative phyllotaxy to a transitional (3, 5) contact pattern which is maintained through sepal production. Formation of a 5(1, 1) whorl of petal primordia establishes a (5, 8) contact pattern with the sepal primordia. Subsequent initiation of stamen primordia, in spiral sequence, results in (5, 8, 13) triple contacts between petal and stamen primordia. The stamen primordia and carpel primordia arrangement is characterized by a (8, 13) contact parastichy pattern of phyllotaxy. Through ontogeny the volume of the shoot apex progressively increases but the shape of the apex, described by a second degree polynomial, remains constant. The plastochron and the relative plastochron rates of radial and vertical displacement of primordia progressively decrease during transition but there is no alteration of the chronological rate of apical expansion. The change in contact parastichy phyllotaxy through ontogeny is interpreted as a change in the relative positions of primordia insertion on the apex resulting from an increase in apical volume and an increased rate of primordia initiation.     

Physical phenomenology of phyllotaxis

We propose an evolutionary mechanism of phyllotaxis, regular arrangement of leaves on a plant stem. It is shown that the phyllotactic pattern with the Fibonacci sequence has a selective advantage, for it involves the least number of phyllotactic transitions during plant growth.     

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.     

Noise and robustness in phyllotaxis

A striking feature of vascular plants is the regular arrangement of lateral organs on the stem, known as phyllotaxis. The most common phyllotactic patterns can be described using spirals, numbers from the Fibonacci sequence and the golden angle. This rich mathematical structure, along with the experimental reproduction of phyllotactic spirals in physical systems, has led to a view of phyllotaxis focusing on regularity. However all organisms are affected by natural stochastic variability, raising questions about the effect of this variability on phyllotaxis and the achievement of such regular patterns. Here we address these questions theoretically using a dynamical system of interacting sources of inhibitory field. Previous work has shown that phyllotaxis can emerge deterministically from the self-organization of such sources and that inhibition is primarily mediated by the depletion of the plant hormone auxin through polarized transport. We incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis--the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles--and we investigated whether a secondary inhibitory field filters out defects. Our results are consistent with available experimental data and yield a prediction of the main source of stochasticity during organogenesis. Our model can be related to cellular parameters and thus provides a framework for the analysis of phyllotactic mutants at both cellular and tissular levels. We propose that secondary fields associated with organogenesis, such as other biochemical signals or mechanical forces, are important for the robustness of phyllotaxis. More generally, our work sheds light on how a target pattern can be achieved within a noisy background.     

Formation of Pseudowhorls inPeperomia verticillata(L.) A. Dietr. Shoots Exhibiting Various Phyllotactic Patterns

Pseudowhorls are composed of leaves attached at almost equallevels and separated by single fully elongated internodes. InPeperomiaverticillata, pseudowhorls form regularly in shoots exhibitingboth spiral and truly whorled patterns of phyllotaxis. In spiralsystems, they are composed of successive leaves positioned onthe ontogenetic helix. In whorled phyllotaxis, leaves of twoadjacent whorls occur at almost the same level and this wayform a pseudowhorl. The number of leaves per pseudowhorl dependson the type of phyllotactic pattern and also the system of primordiapacking. In all the shoots, regardless of the type of phyllotaxis,the number of leaves per pseudowhorl equals the number of leafprimordia in physical contact with the apical dome. It is thesame as the higher number in contact parastichy pairs in spiralpatterns or the number of orthostichies in whorled phyllotaxis.The pseudowhorled pattern is already manifested in the arrangementof leaf primordia. In spiral and whorled phyllotaxis the plastochronratio calculated for primordia or whorls belonging to adjacentpseudowhorls is always higher than that calculated for membersof one pseudowhorl. Moreover, angular distances between primordiaof one pseudowhorl in spiral patterns are more uniform thanexpected in Fibonacci phyllotaxis. These observations were madeon plants both growing in pots and culturedin vitro. 6-Benzylaminopurine,a synthetic cytokinin, added to the medium increases the meannumber of leaves per pseudowhorl. It seems that this effectis indirect: phyllotaxis changes first rather than the destinyof a particular internode in a process of selective elongation.Copyright1999 Annals of Botany Company Peperomia verticillata, pseudowhorls, phyllotaxis, shoot apex.     

THE ABPHYL SYNDROME IN ZEA MAYS. I. ARRANGEMENT. NUMBER AND SIZE OF LEAVES

A range of phyllotactic variation in Zea mays has been obtained from progeny derived from a single ‘opposite-leaved’ plant. Some segregants exhibit a form of alternate phyllotaxy with poor separation between nodes, while others duplicate the original decussate condition. Numerous intermediate examples have also been observed. Some have both spiral and opposite arrangements on the same plant; others, which begin their ontogeny with the normal distichous arrangement, switch at different stages of maturity to spiral or decussate arrangement. Leaves from ABPHYL plants are up to one-half the width of comparable normal leaves although their length is similar. Since ABPHYL plants may have twice as many leaves as do normal siblings, total area and dry weight of leaf blades per ABPHYL plant are greater than in normal siblings. Leaf width of both ABPHYL and normal plants correlates well with the number rather than the width of epidermal cells.     

Rice DECUSSATE controls phyllotaxy by affecting the cytokinin signaling pathway

Phyllotaxy is defined as the spatial arrangement of leaves on the stem. The mechanism responsible for this extremely regular pattern is one of the most fascinating enigmas in plant biology. In this study, we identified a gene regulating the phyllotactic pattern in rice. Loss‐of‐function mutants of the DECUSSATE (DEC) gene displayed a phyllotactic conversion from normal distichous pattern to decussate. The dec mutants had an enlarged shoot apical meristem with enhanced cell division activity. In contrast to the shoot apical meristem, the size of the root apical meristem in the dec mutants was reduced, and cell division activity was suppressed. These phenotypes indicate that DEC has opposite functions in the shoot apical meristem and root apical meristem. Map‐based cloning revealed that DEC encodes a plant‐specific protein containing a glutamine‐rich region and a conserved motif. Although its molecular function is unclear, the conserved domain is shared with fungi and animals. Expression analysis showed that several type A response regulator genes that act in the cytokinin signaling pathway were down‐regulated in the dec mutant. In addition, dec seedlings showed a reduced responsiveness to exogenous cytokinin. Our results suggest that DEC controls the phyllotactic pattern by affecting cytokinin signaling in rice.     

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.     

Excess of nonsynonymous polymorphism at Acph-1 in different gene arrangements of Drosophila subobscura

Nucleotide variation in the Acph-1 gene region was analyzed in a natural population of Drosophila subobscura from Bizerte (Tunisia). The lines studied differed in their gene arrangement for segment I of the O chromosome: 21 lines were O3+4+8, 21 were O3+4+23, and 3 were O3+4. According to chromosomal phylogenies, O3+4 is a central arrangement from which O3+4+8 and O3+4+23 originated. Strong genetic differentiation at Acph-1 was detected among the different arrangements, which is reflected in strong linkage disequilibrium between the variants at informative polymorphic sites and the type of arrangement. Estimates of silent nucleotide diversity are slightly lower within O3+4+23 (pisilent = 0.0166) than within O3+4+8 (pisilent = 0.0228) or O3+4 (pisilent = 0.0234). In contrast, nonsynonymous nucleotide diversity estimates (around 0.1%) are similar in the three arrangements. Most nonsynonymous rare variants are singletons, which results in highly significant Tajima's neutrality tests within the young O3+4+8 and O3+4+23 arrangements. This test is not significant for nonsynonymous mutations within a large Spanish O3+4 sample. In addition, a significant and marginally significant excess of nonsynonymous polymorphism was detected by the McDonald and Kreitman test within O3+4+23 and O3+4+8, respectively. This excess results in a rather high neutrality index (NI = 5.25) when both arrangements are jointly analyzed, in contrast to its value within the old O3+4 arrangement (NI = 1.74). The pattern of variation at Acph-1 within the young arrangements is unusual for nuclear genes and has the same characteristics previously detected in most genes of the mitochondrial genome. Assuming that most nonsynonymous mutations at Acph-1 are under weak negative selection, a smaller effective size of the young arrangements relative to O3+4 might explain the observed results. The relatively low frequency of O3+4+8 and O3+4+23 in the distribution area of D. subobscura, the more recent origin of these arrangements relative to O3+4 and the suppression of recombination in heterokaryotypes might contribute to the relatively small effective size of the young arrangements. Therefore, present results indicate that the differences in effective size and recombination caused by chromosomal arrangements are modulating nonsynonymous variation at Acph-1.     

PHYLLOTAXIS AND VASCULAR ORGANIZATION OF THE CARPELS IN MICHELIA FUSCATA

Tucker , Shirley C. (U. Minnesota, Minneapolis.) Phyllotaxis and vascular organization of the carpels in Michelia fuscata. Amer. Jour. Bot. 48(1): 60–71. Illus. 1961.—Phyllotaxis pattern and vascular organization are closely related in the floral receptacle of Michelia fuscata (Magnoliaceae). The carpels arise in a spiral or helix. They are initiated alternately along each of 7, 8 or 10 helical parastichies according to a complex repetitive sequence. The pattern of the dorsal carpellary trace fusions is orderly for each of the 10 flowers investigated. The dorsal carpellary traces in each parastichy diverge from the same vascular sympodium. Among flowers one finds differing numbers of parastichies, differing angles of divergence, and varying sequences of parastichies which reflect the order of carpel initiation. The angle of divergence, although consistent for any 1 parastichy in a flower, can vary greatly between parastichies. The nature and importance of the organizers which determine appendage position at the apical meristem are considered. Changes in apical size, configuration, and activity are shown to be related to phyllotaxis.     

THE RELATIONSHIPS BETWEEN THE PRIMARY VASCULAR SYSTEM AND PHYLLOTACTIC PATTERNS OF ANAGALLIS ARVENSIS (PRIMULACEAE)

The various primary vascular systems of shoots of Anagallis arvensis L. (Primulaceae) can be distinguished in relation to the number of leaves (two, three, or four) at each node. In this study, shoot segments (single intemodes and the nodes above them) were examined. The arrangement of segments within shoots was also recorded. The vasculature forms a closed system with the number of sets of bundles usually equal to twice the number of leaves. Irregularities are found in the following features of the system: the number of bundles composing leaf half-traces; occurrence of anastomosing bundles; the number of intemodes through which bundles extend; levels of leaf attachment to the stem at the node; and distribution of parenchyma within the vascular cylinder, which determines the number of bundles in sets and the number of bundle sets. The irregularities occur with different frequencies for segments exhibiting different phyllotactic patterns. Comparison of these frequencies leads to the following conclusions: anastomosing bundles occur only in decussate or trimerous shoot segments, whereas sets of bundles united within intemodes and displaced leaves occur only in tetramerous or trimerous ones; decrease of the number of bundles per leaf and displacement of leaves at the nodal level are correlated; variation between segments exhibiting the same phyllotactic pattern is greatest for trimerous, less for tetramerous, and least for decussate segments; the vascular system of decussate shoot segments is more stable than that of the other systems; and trimerous segments seem to be intermediate between the other two segment types.     

Plants expressing a miR164-resistant CUC2 gene reveal the importance of post-meristematic maintenance of phyllotaxy in Arabidopsis

In plants, the arrangement of organs along the stem (phyllotaxy) follows a predictable pattern. Recent studies have shown that primordium position at the meristem is governed by local auxin gradients, but little is known about the subsequent events leading to the phyllotaxy along the mature stem. We show here that plants expressing a miR164-resistant CUP-SHAPED COTYLEDON2 (CUC2) gene have an abnormal phyllotactic pattern in the fully grown stem, despite the pattern of organ initiation by the meristem being normal. This implies that abnormal phyllotaxy is generated during stem growth. These plants ectopically express CUC2 in the stem, suggesting that the proper timing of CUC2 expression is required to maintain the pattern initiated in the meristem. Furthermore, by carefully comparing the phyllotaxy in the meristem and along the mature inflorescence in wild types, we show that such deviation also occurs during wild-type development, although to a smaller extent. We therefore suggest that the phyllotactic pattern in a fully grown stem results not only from the organogenetic activity of the meristem, but also from the subsequent growth pattern during stem development.     

Phyllotactic Pattern Generation: A Conceptual Model

A conceptual model is proposed here that shows how all typesof whorled and peculiar patterns in phyllotaxis derive straightforwardlyfrom normal and anomalous spiral patterns. This is a completemodel of phyllotaxis, integrating the author's interpretativemodel for generating spiral patterns. The paper underlines thata better understanding of the variety of phyllotactic patterns,and of the transitions between them, involves a phylogeneticperspective. It stresses the working hypothesis that spiralpatterns are primitive and that all other patterns, such aswhorled systems, are by-products of evolution from spirality.An important epistemological consequence on mathematical modellingis drawn out of this hypothesis, namely that models of knowledgeor interpretative models, able to take care of the spiral patterns,must be formulated and then followed by simulation, mechanisticor conceptual models that are able to reproduce the transitionsto all other types of patterns. Phyllotaxis, parastichy pair, shoot apex, multijugy, spirality, whorl, modelling, phylogeny, telome theory, Hofmeister's rule     

Role of proline …︁ proline interactions in the packing of collagenlike poly(tripeptide) triple helices

Conformational energy computations were carried out on the packing of two identical collagenlike poly(tripeptide) triple helices in order to determine the energetics of favorable packing arrangements as a function of composition and chain length. The triple helices considered were [CH₃CO-(Gly-Pro-Pro)_nt-NHCH₃]₃ and [CH₃CO-(Gly-Pro-Ala)_nt-NHCH₃]₃, with n_t = 3, 4, and 5. The packing arrangements were characterized in terms of their intermolecular energies and orientation angles Ω₀ of the axes of the two triple helices. For short triple helices (n_t = 3 or 4), many low-energy orientations, with a wide range of values of Ω₀, can occur. When the triple helices are longer (n_t = 5), the only low-energy packing arrangements of two poly(Gly-Pro-Pro) triple helices are those with a nearly parallel orientation of the two helix axes, with Ω₀ ≈ ?10°. This result accounts for the observed parallel (rather than antiparallel) arrangement of collagen molecules in microfibril assembly and stands in contrast to the preferred antiparallel arrangement of a pair of α-helices. Since the preference for a parallel arrangement of these collagenlike triple helices is less pronounced in the case of poly(Gly-Pro-Ala), it appears that this preference is a consequence of the frequent presence of imino acids in position Y of the Gly-X-Y repeating triplet. In poly(Gly-Pro-Ala), most of the low-energy packing arrangements are parallel, but a few arrangements with low energies and high values of |Ω₀| occur. These packing arrangements have a high energy, however, when Pro is substituted for Ala, and thus they are not accessible for collagen with natural amino (imino) acid sequences. The computations reported here account for some of the characteristic features of collagen packing in terms of the local interaction energies of a pair of triple helices.     

Changes in chromosomal polymorphism and global warming: The case of Drosophila subobscura from Apatin (Serbia)

In this study, chromosomal inversion polymorphism data for a natural population of Drosophila subobscura from a swampy region near the town of Apatin (Serbia) were compared with data for the same population collected approximately 15 years earlier. The pattern of chromosomal inversion polymorphism changed over time. There were significant increases in the frequency of characteristic southern latitude ("warm" adapted) chromosomal arrangements and significant decreases in the frequency of characteristic northern latitude ("cold" adapted) chromosomal arrangements in the O and U chromosomes. The chromosomal arrangements O(3+4) and O(3+4) (+) (22) (derived from the O(3+4) arrangement) showed significant increases in 2008 and 2009 with regard to the 1994 sample. There was also a significant increase (～50%) in the U(1) (+) (2) arrangement, while U(1+8) (+) (2) (a typical southern arrangement) was detected for the first time. Since the Apatin swampy population of D. subobscura has existed for a long time in a stable habitat with high humidity that has not been changed by man our results indicate that natural selection has produced chromosomal changes in response to the increase in temperature that has occurred in the Balkan Peninsula of central southeastern European.     

Sequences of symmetry-breaking in phyllotactic transitions

This paper studies the transition of phyllotactic patterns by a group-theoretic approach. Typical phyllotactic patterns are represented here as dotted patterns on a cylinder, where the cylinder is regarded as the stem of a plant and the dots are points where leaves branch from the stem. We can then classify the symmetries of the alternate and opposite phyllotaxis into four types of groups, and clarify sequences of symmetry-breaking among these groups. The sequences turn out to correspond to transition paths of phyllotactic patterns found in the wild. This result shows the usefulness of classification of phyllotactic patterns based on their group symmetries. Moreover, the breaking of reflection symmetry is found to be an important rule for real phyllotactic transitions.