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.     

Patterns of arrangement of lateral appendages on axes of Stigmaria ficoides (Sternberg) Brongniart

The arrangement of lateral insertions has been examined on axes of Stigmaria ficoides . The arrangement can be considered as a phyllotactic pattern made up of parastichies and orthostichies. Orthodox phyllotactic patterns, based on parastichy numbers from the Fibonacci or common accessory series, do not occur. Instead spiral (or multijugate) arrangements occur based on pairs of parastichy numbers such as x and x + 1, x and x + 2, x and x + 3, etc. and x ranges from 12 to 19. Whorled arrangements occur relatively infrequently. Individual axes commonly show frequent changes in pattern. The observations are used to make deductions about the growth and homology of stigmarian axes.     

FLORAL INITIATION AND EARLY DEVELOPMENT IN ERIGERON PHILADELPHICUS (ASTERACEAE)

The order of floral initiation and subsequent organogeny of Erigeron philadelphicus L. (Asteraceae: Astereae) was found to deviate from the acropetal pattern generally reported for the Asteraceae. Light micrographs show periclinal divisions in the first, second, and deeper subsurface layers of cells on the flanks of the inflorescence apex as the earliest evidence of floral initiation. Scanning electron microscope micrographs indicate that the disk flowers appear first and arise as small protuberances approximately one-third of the way up the previously and undifferentiated highly convex inflorescence apex. A succession of disk flowers arises acropetally in a complex anthotaxy characterized by about 21 dextrorse and 12–15 sinistrorse parastichies (although this pattern is obscured at the apex). After one to three disk flowers have been initiated in each parastichy, the first ray flower initials can be seen to initiate in sites proximal to the oldest and largest disk flowers. Additional ray flowers then initiate basipetally following the dextrorse parastichies established by the disk flowers. Overall floral initiation on the inflorescence apex proceeds acropetally for the disk flowers and basipetally for the ray flowers until the available space is filled. Floral development adheres to the same plan—proceeding bidirectionally on the inflorescence meristem with the oldest and most complete flowers of both types located on the equator established at initiation.     

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.     

CELLULAR BASIS FOR GROWTH AND TISSUE DIFFERENTIATION PATTERNS IN LINUM USITATISSIMUM (LINACEAE) STEMS: THE STEM UNIT

The stem unit is defined as the smallest portion of a stem that can duplicate the stem in toto through regular rotations and dilations over successive plastochrons. In stems exhibiting k(m, n) contact parastichy phyllotaxis, the stem unit is delimited vertically and tangentially by the boundaries of four successive leaf primordia along the m-, n-, and (m + n)- parastichies and radially by these boundaries extended to the centroid of the stem. With the stem unit concept, node refers only to the region of actual leaf insertion, rather than the entire transverse level of insertion. Many of the conflicting and complicating aspects of the traditional node-intemode subdivisions of stems are demonstrated, and the utility of the stem unit in circumventing these is illustrated. The stem unit is proposed as a more useful analytic subunit of the stem with which to examine stem growth and tissue differentiation processes than the more traditional node-intemode subdivisions of stems.     

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     

Spatial normalization of one-dimensional electrophoretic gel images

A strategy for using processed, digitized images of one-dimensional electrophoretic gels to facilitate the analysis of large sets of overlapping clones is described. The images are acquired from fluorescently stained gels or from transilluminated gel photographs using a cooled, solid-state charge-coupled device camera. By employing sets of bands in the size-standard lanes as reference points, all the gel images are spatially normalized to a common reference template. After normalization, lane images from different gels can be compared as though the gels had been electrophoresed under identical, uniform-field conditions. Applications of this procedure to the analysis of a large set of overlapping lambda clones from chromosome VII of Saccharomyces cerevisiae and to the estimation of fragment sizes are illustrated.     

Trophic structure and species diversity

Equations derived from a contact pressure model of phyllotaxis are relevant to close packing of equal spheres on a cylindrical surface. They provide a general method of calculating the parameters for microscopic biological structures that are assembled in helical arrangements of protein monomers. In the triple-contact case of hexagonal packing, with km, kn and k(m+n) contact parastichies respectively, where m and n are relatively prime, the divergence angle d and the normalized internode distance r on the k fundamental spirals are completely determined by m, n and k, and formulas are given for calculating them. In the double-contact case of rhombic packing, with km and kn contact parastichies respectively, where m < n, d is a function of r, and the domain of r is the interval between the value of r determined for the triple-contact case of km, kn and k(m+n) parastichies and the value of r determined for the triple-contact case of k(n-m), km and kn parastichies. Here r and d can be determined from the measured ratio of the radius of the cylindrical surface to the radius of the spheres.     

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.     

Mathematical biology of automobile driving: I. The shape of the tracking curve on an empty straight road

The idea was suggested by the author previously (Bull. Math. Biophysics,22, 257–262, 1962) that the keeping of the car close to the center of the lane is a problem of psychophysical discrimination between two conflicting stimuli, namely a stimulus to turn away from the left, resp. right edge of the lane. This is elaborated in the present paper. The effects of discrimination threshold and of the endogenous fluctuations which result in erroneous judgments are discussed. In order that driving should be possible at all, a relation, derived in this paper, must hold between the threshold of discriminationh, the sensitivity coefficientb of the driver to changes in the distance between the car and the edge of the lane, and the width of the lane. General expressions are derived which characterize the stochastic nature of the tracking curve.     

THE SHOOT APICAL ONTOGENY OF THE PICEA ABIES SEEDLING. I. ANATOMY,APICAL DOME DIAMETER,AND PLASTOCHRON DURATION

Developing embryos in immature Picea abies seeds already have well-delineated shoot apical meristems with clearly evident cytohistological zonation. During early seedling development the zonation characteristic of gymnospermous apical meristems is attained. Seedling development is also accompanied by an approximately threefold increase in apical dome diameter. The latter approaches a steady state about 140 days after germination. Seedlings display a spiral phyllotaxis consisting of a contact parastichy system, usually of the primary Fibonacci series. As the seedlings age and apical domes enlarge, higher Fibonacci number-pairs characterize their phyllotaxis. Mathematical analysis of the relation between cumulative leaf number and age revealed that the length of the plastochronic time interval declines from about 18.5 hr to 5.7 hr as seedling age increases from 20 to 140 days.     

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.     

Anodic asymmetry of leaves and flowers and its relationship to phyllotaxis

BACKGROUND AND AIMS: New approaches are needed to evaluate the various hypotheses of phyllotaxis, and an examination of anodic leaf asymmetry may be one such approach. METHODS: Data were collected on the direction of midrib curvature and leaf coil in Syngonium podophyllum, the location of floral buds in Acalypha virginica, the position of secondary leaves of Croton variegatus 'Banana' and the relative size of half-lamina in Aglaonema crispum and Calathea ornata. KEY RESULTS: All five features were exclusively anodic with respect to the direction of the genetic spiral regardless of whether the spiral was clockwise or counterclockwise. CONCLUSIONS: Any phyllotactic mechanism must include some asymmetric component which cannot be explained by the prevalent hypotheses of contact parastichies, inhibitory fields, available space, pressure waves and auxin transport. The most favourable hypothesis is the primary vasculature explanation as it includes an asymmetric feature.     

Single-molecule analysis of the microtubule cross-linking protein MAP65-1 reveals a molecular mechanism for contact-angle-dependent microtubule bundling

Bundling of microtubules (MTs) is critical for the formation of complex MT arrays. In land plants, the interphase cortical MTs form bundles specifically following shallow-angle encounters between them. To investigate how cells select particular MT contact angles for bundling, we used an in vitro reconstitution approach consisting of dynamic MTs and the MT-cross-linking protein MAP65-1. We found that MAP65-1 binds to MTs as monomers and inherently targets antiparallel MTs for bundling. Dwell-time analysis showed that the affinity of MAP65-1 for antiparallel overlapping MTs is about three times higher than its affinity for single MTs and parallel overlapping MTs. We also found that purified MAP65-1 exclusively selects shallow-angle MT encounters for bundling, indicating that this activity is an intrinsic property of MAP65-1. Reconstitution experiments with mutant MAP65-1 proteins with different numbers of spectrin repeats within the N-terminal rod domain showed that the length of the rod domain is a major determinant of the range of MT bundling angles. The length of the rod domain also determined the distance between MTs within a bundle. Together, our data show that the rod domain of MAP65-1 acts both as a spacer and as a structural element that specifies the MT encounter angles that are conducive for bundling.     

Developmental expression patterns of Bcl-2, Bcl-x, Bax, and Bak in teeth

The ontogenic profile of expression of four members of the Bcl-2 family (Bcl-2, Bcl-x, Bax and Bak) was examined in the mouse by immunohistochemistry using paraffin sections. All four members were expressed in changing patterns during critical stages of tooth morphogenesis. Expression was detected in epithelial cell populations including the dental lamina, internal dental epithelium (IDE; differentiating ameloblasts), stratum intermedium and stellate reticulum cells, as well as in the condensed dental mesenchyme. The temporo-spatial localization of the various members of the Bcl-2 family in dental epithelium and mesenchyme showed striking overlapping areas but often their expression patterns differed. In general, contemporaneous co-expression of the Bcl-2 and Bax proteins, and of the Bcl-x and Bak proteins was noted in various types of cells during the developmental process, with the intensity of Bcl-2>Bax and of Bak>Bcl-x. Expression was pronounced at sites where interaction between surface ectoderm and induced mesenchyme takes place, and at the enamel knot, which is regarded as organization/regulating center for tooth development. Around birth, after the structural maturation was accomplished, the expression was down-regulated. The absence of elevated expression of each of these four members of the Bcl-2 family after birth in the teeth suggests that these proteins are relevant during the accomplishment of the basic architecture but not once the structure of the tooth is established.     

Assembly of a polytopic membrane protein structure from the solution structures of overlapping peptide fragments of bacteriorhodopsin.

Three-dimensional structures of only a handful of membrane proteins have been solved, in contrast to the thousands of structures of water-soluble proteins. Difficulties in crystallization have inhibited the determination of the three-dimensional structure of membrane proteins by x-ray crystallography and have spotlighted the critical need for alternative approaches to membrane protein structure. A new approach to the three-dimensional structure of membrane proteins has been developed and tested on the integral membrane protein, bacteriorhodopsin, the crystal structure of which had previously been determined. An overlapping series of 13 peptides, spanning the entire sequence of bacteriorhodopsin, was synthesized, and the structures of these peptides were determined by NMR in dimethylsulfoxide solution. These structures were assembled into a three-dimensional construct by superimposing the overlapping sequences at the ends of each peptide. Onto this construct were written all the distance and angle constraints obtained from the individual solution structures along with a limited number of experimental inter-helical distance constraints, and the construct was subjected to simulated annealing. A three-dimensional structure, determined exclusively by the experimental constraints, emerged that was similar to the crystal structure of this protein. This result suggests an alternative approach to the acquisition of structural information for membrane proteins consisting of helical bundles.     

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.     

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.     

Cellular quantitative analysis of neuroblastoma tumor and splitting overlapping cells

Background

Neuroblastoma Tumor (NT) is one of the most aggressive types of infant cancer. Essential to accurate diagnosis and prognosis is cellular quantitative analysis of the tumor. Counting enormous numbers of cells under an optical microscope is error-prone. There is therefore an urgent demand from pathologists for robust and automated cell counting systems. However, the main challenge in developing these systems is the inability of them to distinguish between overlapping cells and single cells, and to split the overlapping cells. We address this challenge in two stages by: 1) distinguishing overlapping cells from single cells using the morphological differences between them such as area, uniformity of diameters and cell concavity; and 2) splitting overlapping cells into single cells. We propose a novel approach by using the dominant concave regions of cells as markers to identify the overlap region. We then find the initial splitting points at the critical points of the concave regions by decomposing the concave regions into their components such as arcs, chords and edges, and the distance between the components is analyzed using the developed seed growing technique. Lastly, a shortest path determination approach is developed to determine the optimum splitting route between two candidate initial splitting points.

Results

We compare the cell counting results of our system with those of a pathologist as the ground-truth. We also compare the system with three state-of-the-art methods, and the results of statistical tests show a significant improvement in the performance of our system compared to state-of-the-art methods. The F-measure obtained by our system is 88.70%. To evaluate the generalizability of our algorithm, we apply it to images of follicular lymphoma, which has similar histological regions to NT. Of the algorithms tested, our algorithm obtains the highest F-measure of 92.79%.

Conclusion

We develop a novel overlapping cell splitting algorithm to enhance the cellular quantitative analysis of infant neuroblastoma. The performance of the proposed algorithm promises a reliable automated cell counting system for pathology laboratories. Moreover, the high performance obtained by our algorithm for images of follicular lymphoma demonstrates the generalization of the proposed algorithm for cancers with similar histological regions and histological structures.