The theory of phyllotaxis. II. Crystallographic interpretation of the interrelation between lower and superior phyllotaxis forms

Cross-opposite phyllotaxis forms are defined as superior with respect to the alternate ones and verticillate phyllotaxis forms as superior with respect to the opposite ones. Different phyllotaxis forms can be interpreted as a result of stretching of crystal-like structures of the embryo formed by dense packing of rudiments. Based on hypothetical concepts of the properties of plant rudiments and embryos, possible mechanisms of the formation of superior phyllotaxis forms from the lower ones have been analyzed. It was shown that the superior phyllotaxis forms can be considered as the results of additive summation of the lower forms. The theoretical conclusions are confirmed by the examples of polymorphic phyllotaxis in conspecific plants and by the facts of accidental splitting of superior phyllotaxis forms into the corresponding lower forms in nature and in experiment. The mechanisms underlying the formation of multiple forms of helical phyllotaxis have been proposed. The concept of a new type of mixed hexagonal-tetragonal phyllotaxis has been formulated and the mechanism of its formation has been considered. The forms of corn grain packaging in the corncob and leaf arrangement on the strawberry tomato stem are given as examples of true hexagonal-tetragonal phyllotaxis in nature.     

Theory of Phyllotaxis. 2. Crystallographic Interpretation of the Interrelation between Lower and Superior Phyllotaxis Forms

Cross-opposite phyllotaxis forms are defined as superior with respect to the alternate ones and verticillate phyllotaxis forms as superior with respect to the opposite ones. Different phyllotaxis forms can be interpreted as a result of stretching of crystal-like structures of the embryo formed by dense packing of rudiments. Based on hypothetical concepts of the properties of plant rudiments and embryos, possible mechanisms of the formation of superior phyllotaxis forms from the lower ones have been analyzed. It was shown that the superior phyllotaxis forms can be considered as the results of additive summation of the lower forms. The theoretical conclusions are confirmed by the examples of polymorphic phyllotaxis in conspecific plants and by the facts of accidental splitting of superior phyllotaxis forms into the corresponding lower forms in nature and in experiment. The hexagonal-tetragonal type of phyllotaxis was theoretically predicted and found in nature. The mechanism underlying the formation of multiple forms of the helical phyllotaxis was considered.     

Structural theory of phyllotaxis. II. Relationship between lower and higher forms of phyllotaxis

Opposite phyllotaxis forms are defined as superior ones in relation to alternate phyllotaxis forms, and verticillate phyllotaxis forms are defined as superior ones in relation to opposite phyllotaxis forms. On the basis of hypothetical notions about the properties of plant bumps and embryos, the probable mechanisms of creation of superior phyllotaxis forms from the lower ones are analyzed. It is shown that superior phyllotaxis forms can be considered to result from the combination of lower ones and that the superior forms can be split into the corresponding lower ones under artificial or natural influences.     

Theory of phyllotaxis. I. A geometric model for helical forms of consecutive phyllotaxis

We have developed a geometric model for helical forms of consecutive phyllotaxis on the basis of an axiomatic approach. It follows from the model that rudiment growth and the movement of the cylindrical rudiment surface in the absence of a displacement in the direction along the rudiment axis leads to a repeating transition of tetragonal packaging of the rudiment into hexagonal packaging and vice versa. Under these conditions, sequences of rudiments produce left-handed and right-handed helices, the number of which at the circumference of the cylinder corresponds to adjacent numbers of the Fibonacci series. We demonstrate that the left-handed and right-handed isomers of helical forms of the consecutive phyllotaxis appear as a result of the transition of an unstable symmetric structure of the embryo at early developmental stages into stable left-handed or right-handed structures.     

Theory of Phyllotaxis. I. A Geometric Model for Helical Forms of Consecutive Phyllotaxis

We have developed a geometric model for helical forms of consecutive phyllotaxis on the basis of an axiomatic approach. It follows from the model that rudiment growth and the movement of the cylindrical rudiment surface in the absence of a displacement in the direction along the rudiment axis leads to a repeating transition of tetragonal packaging of the rudiment into hexagonal packaging and vice versa. Under these conditions, sequences of rudiments produce left-handed and right-handed helices, the number of which at the circumference of the cylinder corresponds to adjacent numbers of the Fibonacci series. We demonstrate that the left-handed and right-handed isomers of helical forms of the consecutive phyllotaxis appear as a result of the transition of an unstable symmetric structure of the embryo at early developmental stages into stable left-handed or right-handed structures.     

A COMPARATIVE STUDY OF THE PRIMARY VASCULAR SYSTEM OF CONIFERS. I. GENERA WITH HELICAL PHYLLOTAXIS

The primary vascular system of 23 species belonging to 18 genera of conifers with helical phyllotaxis has been investigated with the intent of determining the architecture of the system. Special attention has been given to nodal and subnodal relations of the vascular bundles. The vascular system seems to be composed solely of relatively discrete sympodia, that is, axial vascular bundles from which leaf traces branch unilaterally. Although the discreteness of the sympodia is not immediately apparent because of their undulation and lateral contacts with neighboring ones, close examination, including a statistical analysis of the tangential contacts, seems to reveal that each sympodium maintains its identity throughout. Although two traces may be apparent at nodal levels, the trace supply to a leaf originates, in all species, as a single bundle. An analysis is made of the relationship between the vasculature and the phyllotaxis. It is observed that the direction of trace divergence can be accurately predicted when the direction of the ontogenetic spiral, the angle of divergence of leaf traces, and the number of sympodia are known.     

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.     

Developmental rules in the hematopoietic and immune systems of birds: how general are they?

Fundamental rules about the development of the hematopoietic and immune systems have been established in birds, some of which are reviewed here. The organ rudiments belonging to this system provide the stroma, that has to be seeded by extrinsic stem cells. This particular developmental pattern makes it possible to create chimeric organs with stromal cells and stem cells from different origins. Grafting the thymic epithelium alone in a young embryo is sufficient to induce tolerance to tissues of the same origin as that of epithelium, even in a xenogeneic combination. Stem cells that seed the rudiments during development are born in the embryo rather than in the yolk sac and are responsible for definitive hematopoiesis. Data in frog and mouse indicate that these conclusions may be valid in other classes of vertebrates.     

Basic morphogenetic processes in Hydrozoa and their evolutionary implications: an exercise in rational taxonomy

Species-specific morphology in thecate hydroids is considered as a function of 2 fundamental morphogenetic characteristics: parameters of growth pulsations and the relation between the migratory activities of the endo- and ectodermal cells of the growing tips. Comparative, experimental and modelling data are presented suggesting that increases in the values of these parameters lead to gradual transformation of the narrow tubular rudiments of primitive thecates to the more transversely extended and later bilaterally symmetrical morphologies of advanced forms. There is a corresponding change in the mode of branching, from stolonal through alternate to opposite, with densely packed hydranths and hydrothecae. The relations between the traditional systematic approach to this group and the present ontogenetically based interpretation are discussed.     

Conformational properties of the isolated 1-23 fragment of human hemoglobin alpha-chain

With the purpose of establishing whether, as a general rule, regions of a protein chain that are helical in the native structure maintain, at least partially, the same helical structure when isolated in solution, we have prepared the 1-23 fragment of human hemoglobin alpha-chain, and studied its conformational properties in aqueous solution by CD and 1H-NMR. From the analysis of CD and NMR spectral changes with temperature, salt and addition of trifluoroethanol (TFE) it can be concluded that the 1-23 peptide forms a measurable population (18% at 22 degrees C (pH 5.6) TFE/H2O, 30:70 (v/v)) of an alpha-helix structure that spans the same residues that are helical in the native protein (namely, 6 to 17). These results, taken together with similar ones obtained previously in the 1-19, 21-42 and 50-61 RNAase fragments, support the idea that no helices other than the native ones are actually formed in solution by protein fragments. This implies that the final helical structure of a protein is present from the very beginning of the folding process, and also that such elements of secondary structure can act as primary nucleation centers.     

The purification and properties of nucleoside phosphotransferase from mucosa of chicken intestine

Nucleoside phosphotransferase (nucleotide: 3'-deoxynucleoside 5'-phosphotransferase, EC 2.7.1.77) has been purified from chicken intestine mucosa to apparent homogeneity. The enzyme is represented by a multisubunit protein at different degrees of association. It can dissociate into a component with a marked fall in catalytic activity. The associated forms are similar to the enzyme previously purified from chick embryo as regards: substrate specificity both with respect to nucleoside monophosphate donors and to deoxyribonucleoside acceptors; sigmoidicity in the rate curve with a variable phosphate donor; instability to heat, dilution and lowering of pH; the activating and protecting effect of nucleotides, particularly the diphosphate forms. The dissociated form displays lower Vmax and higher S0.5 than the associated ones; and the Hill constants are always about 1. With this form, nucleotides show only a modest activating effect and do not protect. Mg2+, Mn2+ or Co2+ are required for catalytic activity, whereas the protective effect of nucleotides is independent of divalent metals. Inorganic phosphate stabilizes associated forms of the enzyme, but inhibits its activity by competing with nucleotide effectors. The enzyme behaves also as a phosphohydrolase, particularly with respect to deoxyribonucleoside monophosphates; deoxyuridine and deoxythymidine inhibit hydrolytic activity.     

Morphogenesis of body wall muscle fibers in Enchytraeus minutus

The helical muscle fibers of Enchytraeus minutus (Annelida, Enchytraeidae) have been investigated with respect to their development. We have shown that longitudinal fibers, in the cocoon, begin to develop as platymyarian fibers, then develop into shallow coelomyarian ones and finally, just before hatching, reach a flat circomyarian stage. After hatching, the fibers grow only in size due to an increase in contractile material in the helical sarcomere system. Indications are given as to the ways this process can take place.     

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.     

Conformational properties of the isolated 1–23 fragment of human hemoglobin α-chain

With the purpose of establishing whether, as a general rule, regions of a protein chain that are helical in the native structure maintain, at least partially, the same helical structure when isolated in solution, we have prepared the 1–23 fragment of human hemoglobin α-chain, and studied its conformational properties in aqueous solution by CD and¹H-NMR. From the analysis of CD and NMR spectral changes with temperature, salt and addition of trifluoroethanol (TFE) it can be concluded that the 1–23 peptide forms a measurable population (18% at 22°C (pH 5.6) TFE/H₂O, 30:70 (v/v)) of an α-helix structure that spans the same residues that are helical in the native protein (namely, 6 to 17). These results, taken together with similar ones obtained previously in the 1–19, 21–42 and 50–61 RNAase fragments, support the idea that no helices other than the native ones are actually formed in solution by protein fragments. This implies that the final helical structure of a protein is present from the very beginning of the folding process, and also that such elements of secondary structure can act as primary nucleation centers.     

Sexual and apomictic development in Hieracium

 Most members of the genus Hieracium are apomictic and set seed without fertilization, but sexual forms also exist. A cytological study was conducted on an apomictic accession of H. aurantiacum (A3.4) and also H. piloselloides (D3) to precisely define the cellular basis for apomixis. The apomictic events were compared with the sexual events in a self-incompatible isolate of H. pilosella (P4). All plants were maintained as vegetatively propagated lines each derived from a single plant. Sexual P4 exhibited characteristic events of polygonum-type embryo sac formation, showed no latent apomitic tendencies, and depended upon fertilization to set seed. In contrast, D3 and A3.4 were autonomous aposporous apomicts, forming both embryo and endosperm spontaneously inside an unreduced embryo sac. The two apomicts exhibited distinct mechanisms, but variation was also observed within each apomictic line. Seeds from apomicts often contained more than one embryo. A degree of developmental instability was also observed amongst germinated seedlings and included variation in meristem and cotyledon number, altered phyllotaxis, callus formation, and seedling fusion. In most cases abnormal seedlings developed into normal plants. Such phenomena were not observed following germination of hybrid seeds derived from crosses between sexual P4 and the apomictic plants. The three plants can now be used in inheritance studies and also to investigate the molecular mechanisms controlling apomixis. Received: 11 February 1998 / Revision accepted: 23 July 1998     

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.     

Structural study of poly(beta-benzyl-L-aspartate) monolayers at air-liquid interfaces.

As normally studied, in the solid state or in solution, poly(beta-benzyl-L-aspartate) (PBLA) differs from the other helical polyamino acids in that its alpha-helical conformation is most stable in the left-handed rather than in the right-handed form. The slightly lower energy per residue for the left-handed form in PBLA is easily perturbed, however. The helical screw sense can be inverted in a polar environment and, upon heating above 100 degrees C, a distorted left-handed helix or omega-helix is irreversibly formed. From external reflectance Fourier transform infrared measurements at the air-water interface, the conformation of PBLA in the monolayer state is directly established for the first time. The infrared frequencies of the amide bands suggest that right-handed alpha-helices are formed on the surface of water immediately after spreading the monolayers and independently of the polypeptide conformational distribution in the spreading solution. The right-handed helical form prevails throughout the slow compression of the Langmuir monolayers to collapsed films. The helical screw sense can be reversed by lowering the polarity of the aqueous phase. In addition, an alternate conformation similar to the omega-helix forms on addition of small amounts of isopropanol to the aqueous subphase, and appears to be an intermediate in the helix-helix transition.     

An experimental analysis of factors affecting the localization of embryonic bone marrow

Summary The present investigations have been concerned with factors which determine and influence the localization and development of hemopoietic bone marrow in the embryo mouse and the adult. These studies, which have employed organ cultures and the transplantation of mouse embryo femur and tail rudiments, indicate that the surrounding mesenchyme is required for the normal development of the cartilage rudiment and its ossification, and for the formation and colonization of the marrow cavity. It was suggested that hemopoiesis results from the colonization of the “prepared” marrow cavity by stem cells arising from sources external to the rudiment. The addition of erythropoietin and L-thyroxine produced distinct erythropoietic differentiation in the normally myelocytic embryonic marrow cavity. The significance of the microenvironment present in developing bone rudiments and the initiation of hemopoiesis in stem cells was discussed. A hypothesis was developed to explain marrow localization in adults based on the colonization of bone rudiments which are developing their marrow sites at a time when the blood contains large numbers of colony-forming units.     

Organization of the vascular system in the stems of Diplazium and Blechnum (Filicales)

Detailed analysis of the three-dimensional vascular organization in species of Diplazium and Blechnum indicates that these ferns possess reticulate (dictyostelic) vascular systems that closely reflect the helical phyllotaxis of the shoot. In each species, the vascular pattern shows a specific relationship to the phyllotaxis, so that the phyllotactic fraction can be determined by examination of the number of cauline vascular bundles (meristeles) in cross section of the stem. The number of meristeles in a cross section equals the denominator of the phyllotactic fraction, i.e., the number of foliar orthostichies on the stem. The same numerical relationship also exists in the eusteles of seed plants between the number of axial (sympodial) stem bundles and the phyllotaxis. There is a further parallel between the three-dimensional reticulate pattern of fern dictyosteles and the reticulate patterns that characterize some herbaceous dicotyledons. However, the hypothesized separate origins of seed plant eusteles and fern dictyosteles from protostelic precursors preclude any direct homologies between these similar patterns. The parallel evolution of presumably more physiologically efficient reticulate systems in herbaceous seed plants and in ferns that have only a primary plant body is noteworthy. The similar relationships between the primary stem vascular patterns and phyllotaxy in both ferns and seed plants further emphasize the likely similarity of the morphogenetic events that occur at the shoot apex in these taxonomically disparate groups.