Assessing the benefits of focal pair cryo-electron tomography

Cryo electron tomography provides nanometer-scale information on biological matter preserved in a close-to native state. The resolution of tomograms and structures resolved by sub-tomogram averaging is typically limited by the contrast transfer function of the electron microscope, which is especially critical for thick samples. Here, we report a method to increase the attainable resolution by recording tomographic 'focal pairs', which are pairs of tilt series of the same object acquired in complementary defocus conditions. Low defocus imaging provides high resolution at low contrast, while high defocus imaging yields high contrast at the price of limited resolution. Quantitative assessment of the quality of lipid bilayer reconstructions in the resulting tomograms demonstrates stable resolution preservation beyond 3 nm for cells thicker than 500 nm. Further, in computational simulations on synthetic datasets we show the applicability of the method to sub-tomogram averaging, demonstrating its potential for achieving higher resolution.     

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.     

Classification of electron sub-tomograms with neural networks and its application to template-matching

Classification of electron sub-tomograms is a challenging task, due the missing-wedge and the low signal-to-noise ratio of the data. Classification algorithms tend to classify data according to their orientation to the missing-wedge, rather than to the underlying signal. Here we use a neural network approach, called the Kernel Density Estimator Self-Organizing Map (KerDenSOM3D), which we have implemented in three-dimensions (3D), also having compensated for the missing-wedge, and we comprehensively compare it to other classification methods. For this purpose, we use various simulated macromolecules, as well as tomographically reconstructed in vitro GroEL and GroEL/GroES molecules. We show that the performance of this classification method is superior to previously used algorithms. Furthermore, we show how this algorithm can be used to provide an initial cross-validation of template-matching approaches. For the example of sub-tomogram classification extracted from cellular tomograms of Mycoplasma pneumonia and Spiroplasma melliferum cells, we show the bias of template-matching, and by using differing search and classification areas, we demonstrate how the bias can be significantly reduced.     

An assay for dielectrophoresis: Applications to electromagnetically induced membrane adhesion and fusion

A new assay for dielectrophoresis, consisting of a platinum wire placed along the axis of symmetry of a hollow metal cylinder, was constructed. The main advantage of this device is that because of the simple axisymmetrical electric field the experimental data can be easily interpreted. Preliminary experimental data for adhesion and fusion of red blood cells are reported. The most interesting observation was that fusion of cell membranes can be induced without applying DC electrical pulses, merely because of the dielectrophoretic effect. A possible explanation of this phenomenon is suggested.     

Systematic examination of polymorphism in amyloid fibrils by molecular-dynamics simulation

Amyloid fibrils often exhibit polymorphism. Polymorphs are formed when proteins or peptides with identical sequences self-assemble into fibrils containing substantially different arrangements of the β-strands. We used atomistic molecular-dynamics simulation to examine the thermodynamic stability of a amyloid fibrils in different polymorphic forms by performing a systematic investigation of sequence and symmetry space for a series of peptides with a range of physicochemical properties. We show that the stability of fibrils depends on both sequence and the symmetry because these factors determine the availability of favorable interactions between the peptide strands within a sheet and in intersheet packing. By performing a detailed analysis of these interactions as a function of symmetry, we obtained a series of simple design rules that can be used to determine which polymorphs of a given sequence are most likely to form thermodynamically stable fibrils. These rules can potentially be employed to design peptide sequences that aggregate into a preferred polymorphic form for nanotechnological purposes.     

Maximum likelihood based classification of electron tomographic data

Classification and averaging of sub-tomograms can improve the fidelity and resolution of structures obtained by electron tomography. Here we present a three-dimensional (3D) maximum likelihood algorithm – MLTOMO – which is characterized by integrating 3D alignment and classification into a single, unified processing step. The novelty of our approach lies in the way we calculate the probability of observing an individual sub-tomogram for a given reference structure. We assume that the reference structure is affected by a ‘compound wedge’, resulting from the summation of many individual missing wedges in distinct orientations. The distance metric underlying our probability calculations effectively down-weights Fourier components that are observed less frequently. Simulations demonstrate that MLTOMO clearly outperforms the ‘constrained correlation’ approach and has advantages over existing approaches in cases where the sub-tomograms adopt preferred orientations. Application of our approach to cryo-electron tomographic data of ice-embedded thermosomes revealed distinct conformations that are in good agreement with results obtained by previous single particle studies.     

Symmetry of O-H-O and N-H-N hydrogen bonds in 6-hydroxy-2-formylfulvene and 6-aminofulvene-2-aldimines

The symmetry of the hydrogen bonds in 6-hydroxy-2-formylfulvene and two N,N'-diaryl-6-aminofulvene-2-aldimines is probed by the NMR technique of isotopic perturbation. Observed deuterium-induced 13C NMR isotope shifts at several positions can be attributed to a combination of an intrinsic shift and the perturbation of a tautomeric equilibrium. The most dramatic are at the aldehydic or aldiminic carbon signals, where the observed isotope shift for the unlabeled carbon is +376 or +223 ppb. This large downfield shift is contrary to the small upfield shift expected for a four-bond intrinsic shift and can be attributed only to a perturbation shift. Therefore these intramolecular hydrogen bonds are asymmetric, the proton resides in a double-minimum potential surface, and each molecule exists as a pair of rapidly interconverting tautomers, regardless of solvent. The symmetry of the hydrogen bond is not governed only by the O-O or N-N distance. It is proposed that symmetric hydrogen bonds can be observed in crystalline phases but not as yet in solution because the disorder of the solvation environment induces an asymmetry of the hydrogen bond, whereas a crystal can guarantee a symmetric environment. These results provide no insight into the source of the stabilization attributed to low-barrier hydrogen bonds if they lack the special feature of symmetry.     

Matched-pairs tests of homogeneity with applications to homologous nucleotide sequences

MOTIVATION: Most phylogenetic methods assume that the sequences of nucleotides or amino acids have evolved under stationary, reversible and homogeneous conditions. When these assumptions are violated by the data, there is an increased probability of errors in the phylogenetic estimates. Methods to examine aligned sequences for these violations are available, but they are rarely used, possibly because they are not widely known or because they are poorly understood. RESULTS: We describe and compare the available tests for symmetry of k-dimensional contingency tables from homologous sequences, and develop two new tests to evaluate different aspects of the evolutionary processes. For any pair of sequences, we consider a partition of the test for symmetry into a test for marginal symmetry and a test for internal symmetry. The proposed tests can be used to identify appropriate models for estimation of evolutionary relationships under a Markovian model. Simulations under more or less complex evolutionary conditions were done to display the performance of the tests. Finally, the tests were applied to an alignment of small-subunit ribosomal RNA sequences of five species of bacteria to outline the evolutionary processes under which they evolved. AVAILABILITY: Programs written in R to do the tests on nucleotides are available from http://www.maths.usyd.edu.au/u/johnr/testsym/     

Measurement scale in maximum entropy models of species abundance

The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.     

Larger swordtail females prefer asymmetrical males

Many organisms, including humans, find symmetry more attractive than asymmetry. Is this bias towards symmetry simply a by-product of their detection system? We examined female preference for symmetry of the pigment pattern vertical bars in the swordtail fishes Xiphophorus cortezi and Xiphophorus malinche. We found a relationship between preference for symmetry and female size, with larger and thus older females spending significantly more time with the asymmetrical video animation as compared to the symmetrical video animation. The preference for asymmetry we report demonstrates that even if females can detect symmetrical males better, this does not preclude subsequent selection on females to prefer symmetrical or asymmetrical males. In addition, because the preference was correlated with female size, past studies may have missed preference for either asymmetry and/or symmetry by not examining the relationship between female preference and size/age or by measuring a limited size/age distribution of females. In both of the species of swordtail fishes examined, a high proportion of males are asymmetrical by more than one bar. We suggest that female preference may be maintaining fluctuating asymmetries in these fishes.     

Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

The cause of symmetry is usually subtle, and its study often leads to a deeper understanding of the bearer of the symmetry. To gain insight into the dynamics driving the growth and evolution of genomes, we conducted a comprehensive study of textual symmetries in 786 complete chromosomes. We focused on symmetry based on our belief that, in spite of their extreme diversity, genomes must share common dynamical principles and mechanisms that drive their growth and evolution, and that the most robust footprints of such dynamics are symmetry related. We found that while complement and reverse symmetries are essentially absent in genomic sequences, inverse–complement plus reverse–symmetry is prevalent in complex patterns in most chromosomes, a vast majority of which have near maximum global inverse symmetry. We also discovered relations that can quantitatively account for the long observed but unexplained phenomenon of -mer skews in genomes. Our results suggest segmental and whole-genome inverse duplications are important mechanisms in genome growth and evolution, probably because they are efficient means by which the genome can exploit its double-stranded structure to enrich its code-inventory.     

Symmetry types, systems and their multiplicity in the structure of adenovirus capsid. I. Symmetry networks and general symmetry motifs

Each of the more than 1500 polypeptide molecules of 7 different types building up the adenovirus capsid--probably even those of their amino-acids--are in symmetrical location. Every kind of polypeptide forms a separately also symmetrical network in the capsid distributed according to their functions in the inner and outer side and the inside of the facets and edges, but always in compliance with the icosahedral symmetry. Therefore, each different polypeptide also means a general symmetry motif in the capsid in its own symmetry network. Hexons can be considered as general symmetry motifs in some special association that is because of their environmental position four kinds of hexon types can be found, which are on every facet, next to one another, like three identical groups of four (GOF) according to the three-fold rotational symmetry. Two polypeptides of a peripentonal hexon of each GOF orient toward the penton and the third toward the other penton located further on the same edge. There are two versions of the arrangement of the GOFs: the hexons surround either a polypeptide IX or a polypeptide IlIa. The two versions of GOFs on 20 facets symmetrically recurring 60 times as general hexon symmetry motifs form the capsid in combination with the network of other polypeptides. Ideally, the surface of the hexon trimer shows three-fold rotational and three-fold reflexional symmetries. In the arrangement of hexons in the facets the translational, rotational, horizontal and vertical reflexional symmetry and the combination of these, as well as the glide reflexion and the antisymmetry can be found. Each hexon has six nearest neighbours and every hexon takes part in the construction of three hexon rows. Every facet and every vertex made up of five facets has an antisymmetrical pair located on the opposite side of the capsid. Every triangular facet participates in forming three vertices and every facet has three nearest neighbouring facets. In the facets, the polypeptide subunits of polypeptide IX centered GOF hexons have identical counter-clockwise orientation but the orientation of the neighbouring facets is always opposite compared to each other. On the five-fold symmetry axis, any facet can be "turned on" to the adjacent facet or "rotated" to all the others and will take the symmetry and orientation of the facet it got turned on or rotated to. Thus, every facet together with the polypeptides attached to it shows a twenty-fold symmetry and multiplicity. An other type of symmetry and multiplicity in the capsid is that perpendicular to the 6 five-fold rotation axes run a geodetic (equatorial) ribbon like motif (superfieces) altogether six made up of 10 x 10 triangular facets and bent ten-times with an angle of 36 degrees. A triangular facet participates in forming three ribbon-like motifs, which intersect with each other on the given facet, but the same three motifs intersect repeatedly only on the antisymmetrically located facet.     

Do Antlers Honestly Advertise the Phenotypic Quality of Fallow Buck (Dama dama) in a Lekking Population?

Size and symmetry of secondary sexual traits are supposed to be honest signals of male phenotypic quality in vertebrates. Antler size and symmetry, male quality and mating success have not been fully demonstrated to be correlated in cervids. Such correlations can be particularly intriguing in the case of species adopting costly mating strategies, which imply territorial defence without feeding. In these cases, body condition appears to be crucial at the onset of the rut, and large and symmetrical antlers may be borne by successful males. For these reasons, during four consecutive years, we analysed growth rate, size and symmetry of 26 fallow bucks’ antlers in relation to individual mating strategy and success in a lekking population. Territorial (T) males, which gained higher mating success in the lek, showed a faster antler growth (about 10 g/d per antler) than non‐territorial (NT) males (3.6–5.2 g/d per antler) during the velvet period, and this was likely because of optimized foraging strategies. At the onset of the rut, when antler growth was completed, T males had larger antlers than NT males. Possibly because of worsened body conditions, NT males showed a pronounced antler directional asymmetry, while T males did not. However, no direct link between antler symmetry and mating success was found, thus confirming the ambiguous role of antler asymmetry as an indicator of fitness. The faster the antler growth, the larger its final size and the higher its beholder’s mating success. Our results confirmed that, like groaning and scent marking, antler size reflects social status and dominance in male fallow deer, and therefore represents an honest advertisement of phenotypic quality.     

Evidence against perceptual bias views for symmetry preferences in human faces

Symmetrical human faces are attractive. Two explanations have been proposed to account for symmetry preferences: (i) the evolutionary advantage view, which posits that symmetry advertises mate quality and (ii) the perceptual bias view, which posits that symmetry preferences are a consequence of greater ease of processing symmetrical images in the visual system. Here, we show that symmetry preferences are greater when face images are upright than when inverted. This is evidence against a simple perceptual bias view, which suggests symmetry preference should be constant across orientation about a vertical axis. We also show that symmetry is preferred even in familiar faces, a finding that is unexpected by perceptual bias views positing that symmetry is only attractive because it represents a familiar prototype of that particular class of stimuli.     

Are human preferences for facial symmetry focused on signals of developmental instability?

Humans find symmetrical faces more attractive than are asymmetricalfaces. Evolutionary psychologists claim that our preferencefor symmetry can be explained in the context of mate choicebecause symmetry is an honest indicator of the genetic qualityof potential mates. These arguments assume that asymmetry inhuman faces is fluctuating asymmetry (FA), because this formof asymmetry can be revealing of developmental instability.However, no study has yet examined the characteristics of facialasymmetry. Here we provide the first detailed study of the patternsof asymmetry in human faces. We measured asymmetry in 35 facialtraits. Although some traits had distributions characteristicof FA, many had distributions that characterize directionalasymmetry (DA); on average, both men and women had right hemi-facedominance. For DA traits we used deviations from the mean asymmetryas a measure of developmental instability. Our measures of asymmetryaccounted for a moderate proportion of the variance in perceivedsymmetry. Importantly, only FAs and random deviations from DAcontributed to people's perception of symmetry. DA was not importantin symmetry judgments. Faces rated as symmetrical were alsorated as attractive. Random deviations from DA were weakly relatedto women's attractiveness judgments of men's faces. DAs didnot influence attractiveness judgments. Our data suggest thatpeople focus on aspects of facial asymmetry that may be revealingof developmental instability. Further studies that isolate FAfrom other forms of asymmetry are required to accurately assessthe influence of developmental instability on the quality ofindividuals and its potential role in mate preferences.     

The absolute efficiency of perceptual decisions

Our perceptions of the world around us are stable and reliable. Is this because the mechanisms that yield them are crude and insensitive and thus immune to false responses? Or is it because a statistical censor that blocks unreliable messages intervenes between the signals from our sense organs and our knowledge of them? This question can be answered by measuring the efficiency with which statistical information is utilized in perception. It is shown that mirror symmetry can be detected in displays of otherwise random dots with an efficiency of up to 50%; thus the statistical mechanisms are not crude and insensitive, and this aspect of sensory physiology and psychology may deserve more attention.     

Symmetry: Modeling the Effects of Masking Noise,Axial Cueing and Salience

Symmetry detection is an interesting probe of pattern processing because it requires the matching of novel patterns without the benefit of prior recognition. However, there is evidence that prior knowledge of the axis location plays an important role in symmetry detection. We investigated how the prior information about the symmetry axis affects symmetry detection under noise-masking conditions. The target stimuli were random-dot displays structured to be symmetric about vertical, horizontal, or diagonal axes and viewed through eight apertures (1.2° diameter) evenly distributed around a 6° diameter circle. The information about axis orientation was manipulated by (1) cueing of axis orientation before the trial and (2) varying axis salience by including or excluding the axis region within the noise apertures. The percentage of correct detection of the symmetry was measured at for a range of both target and masking noise densities. The threshold vs. noise density function was flat at low noise density and increased with a slope of 0.75–0.8 beyond a critical density. Axis cueing reduced the target threshold 2–4fold at all noise densities while axis salience had an effect only at high noise density. Our results are inconsistent with an ideal observer or signal-to-noise account of symmetry detection but can be explained by a multiple-channel model is which the response in each channel is the ratio between the nonlinear transform of the responses of sets of early symmetry detectors and the sum of external and intrinsic sources of noise.     

The incorporation of the A2 protein to produce novel Qβ virus-like particles using cell-free protein synthesis

Virus-like particles (VLPs) have been employed for a number of nanometric applications because they self-assemble, exhibit a high degree of symmetry, and can be genetically and chemically modified. However, high symmetry does not allow for a single unique modification site on the VLP. Here, we demonstrate the co-expression of the cytotoxic A2 protein and the coat protein of the bacteriophage Qβ to form a nearly monodispersed population of novel VLPs. Cell-free protein synthesis allows for direct access and optimization of protein-synthesis and VLP-assembly. The A2 is shown to be incorporated at high efficiency, approaching a theoretical maximum of one A2 per VLP. This work demonstrates de novo production of a novel VLP, which contains a unique site that has the potential for future nanometric engineering applications.     

Symmetric multilayer megampere X-pinch

Raising the power of X-ray emission from an X-pinch by increasing the pinch current to the megampere level requires the corresponding increase in the initial linear mass of the load. This can be achieved by increasing either the number of wires or their diameter. In both cases, special measures should be undertaken to prevent the formation of a complicated configuration with an uncontrolled spatial structure in the region of wire crossing, because such a structure breaks the symmetry of the neck formed in the crossing region, destabilizes plasma formation, and degrades X-ray generation. To improve the symmetry of the wire crossing region, X-pinch configurations with a regular multilayer arrangement of wires in this region were proposed and implemented. The results of experiments with various symmetric X-pinch configurations on the COBRA facility at currents of ∼1MA are presented. It is shown that an X-pinch with a symmetric crossing region consisting of several layers of wires made of different materials can be successfully used in megampere facilities. The most efficient combinations of wires in symmetric multilayer X-pinches are found in which only one hot spot forms and that are characterized by a high and stable soft X-ray yield.     

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.