Information, discrimination and divergence in cytology. V. General symmetry of total discrimination and total divergence.

Total discrimination and divergence are derived from Baye's theorem and based on backward (a posteriori) probabilities. Total forward (a priori) discrimination and divergence can be computed from a test matrix from which total backward discrimination and divergence were calculated for optimization of the classifications of gynecologic cytology (Papanicolaou smears) and quality control in a laboratory. The total forward discrimination and divergence appears to behave in parallel with the total backward discrimination and divergence, and the discrepancies in the backward and forward discrimination/divergence were the smallest near the optimum classification scheme. Conversely, the discrepancies between backward and forward discrimination and divergence may be helpful in finding the best classification scheme for gynecologic cytology. The general symmetries of the total backward and forward discrimination/divergence may be related to the human cognitive process of preferring symmetry and to the historic process in which cytologic classification followed histologic classification and continuously checked for matches in two directions--i.e., from histology to cytology and vice versa--thus resulting in the preservation of symmetry.     

The structures of barium hexafluorosilicate and cesium hexafluororhenate(V)

The crystal structure of CsReF₆, together with a reinvestigation of that of BaSiF₆, is reported. Both have been determined from single crystal three-dimensional X-ray diffraction data. The structure of BaSiF₆ has been found to conform to the initially assigned space group R$\text{3}$m, contrary to the suggestions of other workers. The unit cell of BaSiF₆ has the dimensiona a_hex 7.189(1), c_hex 7.015(1) Å; Z = 3. Refinement by a least squares method gave R 0.0079 and R_w 0.0077. Crystals of CsReF₆ belong to the lower symmetry rhombohedral space group R$\text{3}$. The unit cell has the dimensions a_hex 7.853(1), c_hex 8.140(1) Å; Z = 3. Refinement gave R 0.031 and R_w 0.030. The lowering of symmetry is caused by rotation of the ReF₆^? octahedra about the 3-fold axis through each Re atom, causing CsReF₆ to have the KOsF₆ structure.     

The functional geometry of local and horizontal connections in a model of V1.

A mathematical model of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the geometry of local and long-range horizontal connections. Each hypercolumn is modeled as a network of interacting excitatory and inhibitory neural populations with orientation and spatial frequency preferences organized around a pair of pinwheels. The pinwheels are arranged on a planar lattice, reflecting the crystalline-like structure of cortex. Local interactions within a hypercolumn generate orientation and spatial frequency tuning curves, which are modulated by horizontal connections between different hypercolumns on the lattice. The symmetry properties of the local and long-range connections play an important role in determining the types of spontaneous activity patterns that can arise in cortex.     

Surface topography of the p3 and p6 annexin V crystal forms determined by atomic force microscopy

Annexin V is a member of a family of structurally homologous proteins sharing the ability to bind to negatively charged phospholipid membranes in a Ca(2+)-dependent manner. The structure of the soluble form of annexin V has been solved by X-ray crystallography, while electron crystallography of two-dimensional (2D) crystals has been used to reveal the structure of its membrane-bound form. Two 2D crystal forms of annexin V have been reported to date, with either p6 or p3 symmetry. Atomic force microscopy has previously been used to investigate the growth and the topography of the p6 crystal form on supported phospholipid bilayers (Reviakine et al., 1998). The surface structure of the second crystal form, p3, is presented in this study, along with an improved topographic map of the p6 crystal form. The observed topography is correlated with the structure determined by X-ray crystallography.     

Contextual modulation of V1 receptive fields depends on their spatial symmetry

The apparent receptive field characteristics of sensory neurons depend on the statistics of the stimulus ensemble—a nonlinear phenomenon often called contextual modulation. Since visual cortical receptive fields determined from simple stimuli typically do not predict responses to complex stimuli, understanding contextual modulation is crucial to understanding responses to natural scenes. To analyze contextual modulation, we examined how apparent receptive fields differ for two stimulus ensembles that are matched in first- and second-order statistics, but differ in their feature content: one ensemble is enriched in elongated contours. To identify systematic trends across the neural population, we used a multidimensional scaling method, the Procrustes transformation. We found that contextual modulation of receptive field components increases with their spatial extent. More surprisingly, we also found that odd-symmetric components change systematically, but even-symmetric components do not. This symmetry dependence suggests that contextual modulation is driven by oriented On/Off dyads, i.e., modulation of the strength of intracortically-generated signals. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Symmetry analysis of cell nuclei

An algorithm is described that is used to analyze the two-dimensional spatial symmetry of cell nuclei. The method provides two symmetry features: the symmetry index (SI), which estimates the precise spatial symmetry of a given chromatin component, Cn, and the quadrant symmetry index (QSI), which estimates the number of quadrants being occupied by Cn. A previous analysis is used to show that age-related change in Malpighian tubule nuclei from the adult housefly is associated with significant alterations in the spatial symmetry of low-, medium-, and high-density chromatin components (LDC, MDC, HDC). This included a seven-fold increase in the spatial symmetry of HDC and a shift in the symmetry profile (from highest to lowest degree of symmetry) from LDC-MDC-HDC to MDC-LDC-HDC. The increased spatial symmetry of HDC suggests that it occurs at new nuclear sites as the fly ages and that these sites are distributed over approximately 60% of the chromosome population.     

Symmetries and homologies of Geomerida

The symmetry of Earths life cover (Geomerida) was described generally by L.A. Zenkevich (1948). It coincides with the symmetry of geographic cover. Its symmetry elements are equatorial plane and three meridonal planes corresponded to oceans and continents. The hypsographic curve with point of inflection (symmetry element) on 3 km depth line should be added to these elements. The plankton and benthos communities as well as fauna of taxons are distributed symmetrically according these symmetry elements. Zenkevich model was successfully extrapolated to plankton by K.V. Beklemishev (1967, 1969) and to abyssal benthos by Sokolova M.N. (1986). The plankton communities inhabiting symmetrically located macrocirculations are considered as homologous. The character of circulation determines the trophic structure of plankton and benthos. In the case of high productivity of plankton, benthic grazing animals feed on sedimented particles have bilateral symmetric mouthpart. Otherwise they have to acquire food from water column and use cyclomeric mouthpart. Thus, the symmetry of macrocirculations determines the symmetry distribution of benthic animals with two major symmetries of mouthparts. The peculiarities of organisms' symmetry are discussed in the context of Pierre Curie principle and the ideas of K.V. Beklemishev concerning evolution of morphological axes.     

Symmetry of priapulids (Priapulida). 1. Symmetry of adults

Priapulids possess a radial symmetry that is remarkably reflected in both external morphology and internal anatomy. It results in the appearance of 25-radial (a number divisible by five) symmetry summarized as a combination of nonaradial, octaradial, and octaradial (9+8+8) symmetries of scalids. The radial symmetry is a secondary appearance considered as an evolutionary adaptation to a lifestyle within the three-dimensional environment of bottom sediment. The eight anteriormost, or primary, scalids retain their particular position because of their innervation directly from the circumpharyngeal brain. As a result of a combination of the octaradial symmetry of primary scalids, pentaradial symmetry of teeth, and the 25-radial symmetry of scalids, the initial bilateral symmetry remains characterized by the single sagittal plane.     

Symmetry and entropy of biological patterns: discrete Walsh functions for 2D image analysis

To quantify symmetry and entropy inherent in the discrete patterns such as spatial self-organization in cell sorting and mussel bed ecosystems, we introduce the discrete Walsh analysis. This analysis enables us to estimate the degree of the complicated symmetry, and to extract the symmetry from the pattern that seems to be asymmetric. The results obtained in this paper are summarized as follows. (I) The geometrical patterns of the cell sorting become systematic with the predominance of the particular symmetry. This implies that not only the entropy but also the particular symmetry can decrease in the biological process. (II) The magnitude of the symmetry is related to the absolute value of the adhesion, and the type of the symmetry is related to the sign of the adhesion. That is, centro-symmetry dominates in the cell sorting pattern caused by large negative adhesion, and double symmetry dominates in the pattern caused by large positive adhesion. (III) Spatial self-organization in mussel bed is accompanied by the decreasing of the centro-symmetry. This implies that the positive "adhesion" between mussel individuals increases with time. (IV) In the biological process, the Curie symmetry breaking occurs at intervals.     

Dead-end evolution of the Cnidaria as deduced from 5S ribosomal RNA sequences

Using nucleotide sequences of 5S ribosomal RNAs from 2 hydrozoan jellyfishes, 3 scyphozoan jellyfishes and 2 sea anemones, a phylogenetic tree of Cnidaria has been constructed to elucidate the evolutionary relationships of radial and bilateral symmetries. The 3 classes of Cnidaria examined herein belong to one branch, which does not include other metazoan phyla such as the Platyhelminthes. The Hydrozoa (having radial symmetry without septa) and the Scyphozoa (having radial symmetry with septa) are more closely related to each other than to the Anthozoa (having bilateral symmetry with septa). In classical taxonomy, multicellular animals are considered to have evolved through organisms with radial symmetry (e.g., Cnidaria) to bilateral symmetry. Our results, however, indicate that the emergence of the Bilateria was earlier than that of the Radiata, suggesting (in opposition to Haeckel's view) that the radial symmetry of Cnidaria is an evolutionary dead end.     

Yeast V1-ATPase: affinity purification and structural features by electron microscopy

V1-ATPase from the yeast Saccharomyces cerevisiae was purified via a FLAG affinity tag introduced into the N terminus of the G subunit. The preparation migrated as a single band in native gel electrophoresis and contained subunits ABCDEFGH (with subunit C present at substoichiometric amounts) as determined by matrix-assisted laser desorption ionization time-of-flight mass spectrometry. The initial specific Ca-ATPase activity was approximately 6 micromol/min/mg. The structure of the yeast V1-ATPase was studied by electron microscopy of negatively stained and frozen hydrated samples. A 25-A resolution three-dimensional model of the complex was calculated from two-dimensional projections by the angular reconstitution technique. The model shows six elongated densities arranged in pseudo-3-fold symmetry around a large central cavity. At the top of the molecule, various protrusions can be seen. At the bottom of the complex, two large masses are visible that are connected to the main body of the molecule. Comparison of the yeast V1 structure with the structure of the intact V1V0-ATPase from bovine brain clathrin-coated vesicles (Wilkens, S., Vasilyeva, E., and Forgac, M. (1999) J. Biol. Chem. 274, 31804-31810) indicates that the structure of the isolated V1 from yeast is very similar to the structure of the V1 domain in the intact V-ATPase complex.     

The Mirror-Type Internal Symmetry in the Primary Structure of Proteins: Detection and Functional Role (Review)

This review summarized the data obtained by the author in studies on internal symmetry of the mirror type in primary structures of proteins. The methods for detection of symmetric segments in amino acid sequences are analyzed: (1) the method based on analysis of sequences of roots of amino acid codons; (2) the dot matrix method; (3) the method of internal symmetry scanning. The results of studies of internal symmetry in enzymes and signaling proteins are presented. The probable role of the internal symmetry in the structural-functional organization of proteins is discussed.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity on a (much) slower time scale. This paper examines the effect of STDP in a recurrently connected network stimulated by external pools of input spike trains, where both input and recurrent synapses are plastic. Our previously developed theoretical framework is extended to incorporate weight-dependent STDP and dendritic delays. The weight dynamics is determined by an interplay between the neuronal activation mechanisms, the input spike-time correlations, and the learning parameters. For the case of two external input pools, the resulting learning scheme can exhibit a symmetry breaking of the input connections such that two neuronal groups emerge, each specialized to one input pool only. In addition, we show how the recurrent connections within each neuronal group can be strengthened by STDP at the expense of those between the two groups. This neuronal self-organization can be seen as a basic dynamical ingredient for the emergence of neuronal maps induced by activity-dependent plasticity.     

Emergence of symmetry breaking in fucoid zygotes

Fucoid zygotes are model cells for the study of symmetry breaking in plants. After fertilization, their initial spherical symmetry reduces to an axial symmetry, even in the absence of any external cue. This indicates that zygotes have an intrinsic ability to break symmetry in a way that is solely dependent on their internal biochemical and/or biophysical state. In our opinion, symmetry breaking is a self-organized process. It arises around the fucoid zygotes from the ion dynamics through channels (voltage-dependent calcium channels and a potassium leak) and outside the membrane (electrodiffusion owing to slower calcium diffusion compared with potassium). The robustness of this self-organized process and its lability ensure its relevance in plants where symmetry breaking is correlated with transcellular ion currents.     

A feature-based model of symmetry detection

Symmetry detection is important for many biological visual systems, including those of mammals, insects and birds. We constructed a symmetry-detection algorithm with two stages: location of the visually salient features of the image, then evaluating the symmetry of these features over a long range, by means of a simple Gaussian filter. The algorithm detects the axis of maximum symmetry for human faces (or any arbitrary image) and calculates the magnitude of the asymmetry. We have evaluated the algorithm on the dataset of Rhodes et al. (1998 Psychonom. Bull. Rev. 5, 659-669) and found that the algorithm is able to discriminate small variations of symmetry created by computer-manipulating the symmetry levels in individual faces, and that the values measured by the algorithm correlate well with human psycho-physical symmetry ratings.     

Tilt aftereffects generated by symmetrical dot patterns with two or four axes of symmetry

This paper follows from studies by Joung, van der Zwan and Latimer (2000) in which symmetrical dot patterns with one axis of symmetry were used to produce tilt aftereffects (TAEs). The present paper investigates TAE functions produced by symmetrical dot patterns with multiple axes of symmetry. In Experiments 1 and 2, TAE functions produced by dot patterns with two axes of symmetry were compared with TAE functions produced by line stimuli arranged in the same orientation and location as the axes of symmetry in the dot patterns. Similar functions were found. In Experiments 3 and 4, functions produced by dot patterns with four axes of symmetry were compared with functions produced by line stimuli arranged in the same orientation and location as the four axes of symmetry. Again, similar functions were found. These experiments demonstrate that line stimuli and dot stimuli produce similar TAE functions. The implications of these results are discussed.     

Structural analysis of the S-Layer of Lampropedia hyalina

The two-dimensional (2D) structure of the regularly structured surface layer (S-layer) of the gram-negative eubacterium Lampropedia hyalina has been determined at the molecular level to a nominal resolution of 2.1 nm by transmission electron microscopy and digital image processing. The inner, or “perforate,” layer consists of dimeric block-shaped units located at two-fold symmetry axes. These morphological dimers associate around three-fold symmetry axes to form a continuous layer with p6 symmetry and a lattice constant of 14.6 ± 0.4 nm. Scanning transmission electron microscopy (STEM) yields a mass-per-area (MPA) value for the perforate layer of 3.5 kDa/nm². The outer, or “punctate,” layer is composed of long, roughly cylindrical units centered on six-fold symmetry axes, which are connected by six fine linking arms joining at the three-fold symmetry axes to create a hexagonal layer with a lattice constant of 25.6 ± 0.5 nm. The MPA of the “composite”-i.e., perforate plus punctate—layer is 10.2 kDa/nm².     

Symmetry and the tentacular apparatus in Cnidaria

Comparative analysis provides evidence that bilateral symmetry is a primary character of Cnidaria. All anthozoan taxa are characterized by bilateral symmetry. The anthozoan pharyngeal plane is a plane of bilateral symmetry of mesenteries and, at the same time, it is a plane of bilateral symmetry of regulatory gene expression in anthozoan morphogenesis. In Medusozoa, the bilateral symmetry is replaced by radial symmetry, but some hydrozoans (for example, Corymorphidae) demonstrate bilateral symmetry. The bilateral symmetry of Cnidaria is thought to be inherited from the common ancestors of both cnidarians and triploblastic bilaterians. The secondary radial symmetry of Cnidaria evidently is a result of the adaptation to the sessile mode of life. The presence of both the marginal and labial rings of tentacles is supposed to be a plesiomorphic character of Cnidaria. In some groups of cnidarians, one of the tentacle rings may be reduced.     

Higher-level mechanisms detect facial symmetry

The role of symmetry detection in early visual processing and the sensitivity of biological visual systems to symmetry across a wide range of organisms suggest that symmetry can be detected by low-level visual mechanisms. However, computational and functional considerations suggest that higher-level mechanisms may also play a role in facial symmetry detection. We tested this hypothesis by examining whether symmetry detection is better for faces than comparable patterns, which share low-level properties with faces. Symmetry detection was better for upright faces than for inverted faces (experiment 1) and contrast-reversed faces (experiment 2), implicating high-level mechanisms in facial symmetry detection. In addition, facial symmetry detection was sensitive to spatial scale, unlike low-level symmetry detection mechanisms (experiment 3), and showed greater sensitivity to a 45 degrees deviation from vertical than is found for other aspects of face perception (experiment 4). These results implicate specialized, higher-level mechanisms in the detection of facial symmetry. This specialization may reflect perceptual learning resulting from extensive experience detecting symmetry in faces or evolutionary selection pressures associated with the important role of facial symmetry in mate choice and 'mind-reading' or both.     

The chirality of ground DNA knots and links.

The chirality of ground DNA knots and links is described and characterized in terms of color symmetry groups (CSG), i.e. color symmetry groups I and II, which correspond to topochirality (topological chirality) and topoachirality (topological achirality) which bear an uncanny resemblance to point groups I (proper) and point groups II (improper) used for testing geochirality (geometrical chirality) and geoachirality (geometrical achirality), respectively. By regarding these two crossing modes in mirror images as white and black vertices, DNA knots and links with minimal crossings can be mapped to vertex-bicolored graphs under a working hypothesis that DNA knots and links exist in ground states with minimal energy m0. The color symmetry group of a vertex-bicolored graph G is defined as the set of all permutations and permutation asymmetrizations of the vertices of G that preserve its topology (connectivity), where asymmetrization, denoted as (a), is the operation of changing vertices' colors, and a permutation followed by an (a) is a permutation asymmetrization. The color symmetry groups I contains only permutations, whereas color symmetry groups II comprise permutation asymmetrizations as well as permutations. Four DNA knots and links in nature are analyzed and tabulated consisely. In addition, the well-known figure-of-eight knot and Borromean rings are discussed in much the same way.