Essays on the application of nonclassical symmetries to natural biomorphs

The following symmetries are conventionally termed "nonclassical": conformal symmetry, inversion symmetry, Mikheev homology, curvilinear symmetry, colour symmetry, and antisymmetry. These symmetries are applicable to biomorphs differing in linear dimensions and proportions (such as the shells of bivalves, crustaceans, diatoms, etc.) and to such three-dimensional biomorphs as gastropod shells. These three-dimensional objects used to be substituted so far with two-dimensional images. The shift transformation causing inhomogeneous deformations is discussed in the framework of Mikheev homologies. Antisymmetry and colour symmetry are discussed by the example of flowers, duckweed plants, and the crustacean chela. Early stages of cleavage, like colloid crystals, may be represented as polyhedrons. They have Euler characteristics and face symbols, and, because of this, stages of cleavage may have symmetries of crystals. Mastering nonclassical symmetries may promote the progress of biosymmetrics. The potential of discrete (arithmetical) biomorphology in taxonomy and the potential of continuous (geomertical) biomorphology in biosymmetrics are discussed.     

A Note on the Manipulation of Flower Symmetry inAntirrhinum majus

Treatments consisting of maceration of the centre of the shootapical meristem or localized application of the plant hormone,indoleacetic acid (IAA), to apical flower buds or the estimatedcentre of the shoot apex were made to test their effect, ifany, on flower shape or symmetry. Both types of treatment affectedflower symmetry. IAA treatment was most successful, but it alsoaffected the completeness of the flower, producing a small numberof reduced flowers. Alteration of symmetry was, however, themain response to treatment.Copyright 1999 Annals of Botany Company Antirrhinum majusL., flower symmetry mutants, microsurgical and microhormonal treatments, apical meristem, flower buds.     

Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Background

Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.

Results

We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.

Conclusions

The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.     

Structure and mechanism of imidazoleglycerol-phosphate dehydratase

The structure of A. thaliana imidazoleglycerol-phosphate dehydratase, an enzyme of histidine biosynthesis and a target for the triazole phosphonate herbicides, has been determined to 3.0 A resolution. The structure is composed of 24 identical subunits arranged in 432 symmetry and shows how the formation of a novel dimanganese cluster is crucial to the assembly of the active 24-mer from an inactive trimeric precursor and to the formation of the active site of the enzyme. Molecular modeling suggests that the substrate is bound to the manganese cluster as an imidazolate moiety that subsequently collapses to yield a diazafulvene intermediate. The mode of imidazolate recognition exploits pseudosymmetry at the active site arising from a combination of the assembly of the particle and the pseudosymmetry present in each subunit as a result of gene duplication. This provides an intriguing example of the role of evolution in the design of Nature's catalysts.     

Trends in flower symmetry evolution revealed through phylogenetic and developmental genetic advances

A striking aspect of flowering plant (angiosperm) diversity is variation in flower symmetry. From an ancestral form of radial symmetry (polysymmetry, actinomorphy), multiple evolutionary transitions have contributed to instances of non-radial forms, including bilateral symmetry (monosymmetry, zygomorphy) and asymmetry. Advances in flowering plant molecular phylogenetic research and studies of character evolution as well as detailed flower developmental genetic studies in a few model species (e.g. Antirrhinum majus, snapdragon) have provided a foundation for deep insights into flower symmetry evolution. From phylogenetic studies, we have a better understanding of where during flowering plant diversification transitions from radial to bilateral flower symmetry (and back to radial symmetry) have occurred. From developmental studies, we know that a genetic programme largely dependent on the functional action of the CYCLOIDEA gene is necessary for differentiation along the snapdragon dorsoventral flower axis. Bringing these two lines of inquiry together has provided surprising insights into both the parallel recruitment of a CYC-dependent developmental programme during independent transitions to bilateral flower symmetry, and the modifications to this programme in transitions back to radial flower symmetry, during flowering plant evolution.     

The influence of floral symmetry,dependence on pollinators and pollination generalization on flower size variation

Background and Aims

The pollinator-mediated stabilizing selection hypothesis suggests that the specialized pollination system of zygomorphic flowers might cause stabilizing selection, reducing their flower size variation compared with actinomorphic flowers. However, the degree of ecological generalization and of dependence on pollinators varies greatly among species of both flower symmetry types and this may also affect flower size variation.

Methods

Data on 43 species from two contrasting communities (one alpine and one lowland community) were used to test the relationships and interactions between flower size phenotypic variation, floral symmetry, ecological pollination generalization and species'' dependence on pollinators.

Key Results

Contrary to what was expected, higher flower size variation was found in zygomorphic than in actinomorphic species in the lowland community, and no difference in flower size variation was found between symmetry types in the alpine community. The relationship between floral symmetry and flower size variation depended on ecological generalization and species'' dependence on pollinators, although the influence of ecological generalization was only detected in the alpine community. Zygomorphic species that were highly dependent on pollinators and that were ecologically specialized were less variable in flower size than ecologically generalist and selfing zygomorphic species, supporting the pollinator-mediated stabilizing selection hypothesis. However, these relationships were not found in actinomorphic species, probably because they are not dependent on any particular pollinator for efficient pollination and therefore their flower size always shows moderate levels of variation.

Conclusions

The study suggests that the relationship between flower size variation and floral symmetry may be influenced by population-dependent factors, such as ecological generalization and species'' dependence on pollinators.     

Projection structure of a plant vacuole membrane aquaporin by electron cryo-crystallography

The water channel protein alpha-TIP is a member of the major intrinsic protein (MIP) membrane channel family. This aquaporin is found abundantly in vacuolar membranes of cotyledons (seed storage organs) and is synthesized during seed maturation. The water channel activity of alpha-TIP can be regulated by phosphorylation, and the protein may function in seed desiccation, cytoplasmic osmoregulation, and/or seed rehydration. Alpha-TIP was purified from seed meal of the common bean (Phaseolus vulgaris) by membrane fractionation, solubilization in diheptanoylphosphocholine and anion-exchange chromatography. Upon detergent removal and reconstitution into lipid bilayers, alpha-TIP crystallized as helical tubes. Electron cryo-crystallography of flattened tubes demonstrated that the crystals exhibit plane group p2 symmetry and c222 pseudosymmetry. Since the 2D crystals with p2 symmetry are derived from helical tubes, we infer that the unit of crystallization on the helical lattice is a dimer of tetramers. A projection density map at a resolution of 7.7 A revealed that alpha-TIP assembles as a 60 A x 60 A square tetramer. Each subunit is formed by a heart-shaped ring comprised of density peaks which we interpret as alpha-helices. The similarity of this structure to mammalian plasma membrane MIP-family proteins suggests that the molecular design of functionally analogous and genetically homologous aquaporins is maintained between the plant and animal kingdoms.     

植物花发育的分子机理研究进展

花的发育分为开花决定、花的发端和花器官的发育三个阶段。植物开花由多条途径诱导,包括光周期和光质诱导、春化作用、自主途径、赤霉素诱导、碳水化合物诱导等;植物体本身也存在着开花抑制途径。各种开花诱导途径能激活花分生组织特性基因,使茎端分生组织转变为花分生组织。花器官的发育由器官特性基因决定,这些基因的精确表达需要花分生组织特性基因的激活和多个正、负调节因子的调控;另有一类基因控制着花发育的对称性。花发育机理的研究具有重要的理论意义和广泛的应用前景。     

植物花发育的分子机理研究进展

花的发育分为开花决定、花的发端和花器官的发育三个阶段。植物开花由多条途径诱导,包括光周期和光质诱导、春化作用、自主途径、赤霉素诱导、碳水化合物诱导等;植物体本身也存在着开花抑制途径。各种开花诱导途径能激活花分生组织特性基因,使茎端分生组织转变为花分生组织。花器官的发育由器官特性基因决定,这些基因的精确表达需要花分生组织特性基因的激活和多个正、负调节因子的调控;另有一类基因控制着花发育的对称性。花发育机理的研究具有重要的理论意义和广泛的应用前景。     

Orchids,bilateral symmetry and insect perception

The basic characteristics of orchids, possessing the greatest number of complex floral images of any Angiosperm family, are reviewed. Bilateral symmetry (zygomorphy) is shown by use of information theory techniques to give much greater possibilities for the transmission of visually mediated information than radial symmetry. The difference in information content is further enhanced by motion. The analysis is offered as evidence that the evolution of diversity in complex images, if effected by the unique behavioral specificity of pollinators known as “flower constancy”, is most economically explained by hypothesizing recognition and storage of the total image (“gestalt”) in the agents of natural selection.     

关于一些植物学术语的中译等问题（二）

（１）在各种花对称的分类中,Ｅｈｒｅｎｄｏｒｆｅｒ的分类包括了被子植物花对称方面从原始到进化的各种类型,最为全面广德国学者Ｓｔｒａｓｂｕｒｅｒ在１９１１年编著的第１１版植物学教科书中将具２对称面的荷包牡丹属的花称为ｂｉｌａｔｅｒａｌ或ｄｉｓｙｍｍｅｔｒｉｓｃｈ．这个类型代表了被子植物花的一种较进化的构造,应该予以肯定。由于被指定为描述具２对称面的花的术语ｂｉｌａｔｅｒａｌ与被指定为描述具丑对称面的花的术语ｂｉｌａｔｅｒａｌｌｙｓｙｍｍｅｔｒｉｃａｌ颇为相似,而易引起混淆．为避兔发生混淆．建议不再应用这二术语．在描述具２对称面的花时,选用ｄｉｓｙｍｍｅｔｒｉｃａｌ,中文译为双面对称的,在描述具１对称面的花时,选用ｚｙｇｏｍｏｒｐｈｉｃ（左右对称的）或ｍｏｎｏｓｙｍｍｅｔｒｉｃａｌ,后者的中文可译为单面对称的。（２）赞同将术语ｔｅｐａｌ译为花被片,而不赞同译为“被片”。     

Structure,substrate binding,and symmetry of the mitochondrial ADP/ATP carrier in its matrix-open state

The mitochondrial ADP/ATP carrier (AAC) performs the first and last step in oxidative phosphorylation by exchanging ADP and ATP across the mitochondrial inner membrane. Its optimal function has been shown to be dependent on cardiolipins (CLs), unique phospholipids located almost exclusively in the mitochondrial membrane. In addition, AAC exhibits an enthralling threefold pseudosymmetry, a unique feature of members of the SLC25 family. Recently, its conformation poised for binding of ATP was solved by x-ray crystallography referred to as the matrix state. Binding of the substrate leads to conformational changes that export of ATP to the mitochondrial intermembrane space. In this contribution, we investigate the influence of CLs on the structure, substrate-binding properties, and structural symmetry of the matrix state, employing microsecond-scale molecular dynamics simulations. Our findings demonstrate that CLs play a minor stabilizing role on the AAC structure. The interdomain salt bridges and hydrogen bonds forming the cytoplasmic network and tyrosine braces, which ensure the integrity of the global AAC scaffold, highly benefit from the presence of CLs. Under these conditions, the carrier is found to be organized in a more compact structure in its interior, as revealed by analyses of the electrostatic potential, measure of the AAC cavity aperture, and the substrate-binding assays. Introducing a convenient structure-based symmetry metric, we quantified the structural threefold pseudosymmetry of AAC, not only for the crystallographic structure, but also for conformational states of the carrier explored in the molecular dynamics simulations. Our results suggest that CLs moderately contribute to preserve the pseudosymmetric structure of AAC.     

Flower Symmetry Preferences in Honeybees and their Crab Spider Predators

Flowers exhibit symmetrical patterns, and innate preferences for symmetry in pollinators like honeybees are documented. Most previous studies of symmetry preferences in honeybees, Apis mellifera, tested levels of asymmetry using artificial flowers or stimuli. Here we investigated the effect of flower asymmetry on flower preferences of honeybees in a novel approach using real flowers, incorporating their spectral properties and how the receivers process the visual signals. Importantly, we also tested the response of an ‘eavesdropping’ predator, the crab spider Thomisus spectabilis, that also utilizes the same flower to prey on honeybees. Flowers (Chrysanthemum frutescens) were manipulated to contain asymmetrical and symmetrical patterns, excluding olfactory cues. Both crab spiders and honeybees exhibited a significant preference for symmetrical flowers. Moreover, honeybees exhibited a significant preference for radial symmetry over bilateral symmetry, but no corresponding effect was recorded in crab spiders. Further analyses demonstrated that flower reflectance and orientation of the axis of symmetry did not affect crab spider decisions. Field observations on T. spectabilis revealed that the natural variation in C. frutescens symmetry had no effect on the choice of crab spiders. This indicates that spiders and honeybees may use other flower characteristics, for example, olfactory cues, together with flower symmetry, to make their foraging decisions.