Angle determination for side views in single particle electron microscopy

In order to build a first model in single particle electron microscopy the relative angular orientation of each image of a protein complex must be determined. These orientations can be described by three Eulerian angles. Images of complexes that present the same view can be aligned in two-dimensions and averaged in order to increase their signal-to-noise ratio. Based on these averaged images, several standard approaches exist for determining Euler angles for randomly oriented projection images. The common lines and angular reconstitution methods work well for particles with symmetry while the random conical tilting and related orthogonal tilt reconstruction methods work in most cases but require the acquisition of tilt pairs of images. For the situation where views of particles can be identified that are rotations about a single axis parallel to the grid, an alternative algorithm to determine the orientations of class averages without the need to acquire tilt pairs can be applied. This type of view of a complex is usually called a side view. This paper describes the detailed workings and characterization of an algorithm, named rotational analysis, which uses real-space fiducial markers derived from the averages themselves to determine the Euler angles for side views. We demonstrate how this algorithm works in practice by applying it to a data set of images of affinity-purified bovine mitochondrial ATP synthase.     

Preparation of Steroid Structural Data for the Consideration of Possible Structural-Functional Relationships

A format has been established for the presentation of steroid structural data which may prove to be useful in the consideration of the possible structural-functional relationships of steroids in biological systems. In preparing this format the detailed structural information for all steroids with known crystallographic structures has been computed and summarized, including bond lengths and angles, non-planarity coefficients, dihedral angles, length of the steroid nucleus, and side group inclinations. From the structural point of view it is interesting to note that (a) bond lengths do not differ significantly from the theoretical values, (b) bond angles do differ significantly from the theoretical values, (c) the non-planarity coefficient of the steroid molecule seems to be a function of the number of angular methyl groups but is unaffected by the presence of one heavy atom, (d) except where aromatic bonds are present the non-planarity coefficients of the two-ring and one-ring subdivisions of the steroid nucleus is 0.25 A, (e) the average non-planarity coefficient of the ring joins and “seat” portions of the chairs is 0.03 A, (f) dihedral angles deviate from the theoretically expected values and also show wide variation in the steroids studied, (g) the length of the steroid nucleus is variable, (h) analysis of side group inclination data must be deferred until more steroid structural information is available. From the biological point of view it is currently impossible to estimate the importance of each steroid structural feature in determining physiological function.     

Development of the compound eyes of dragonflies (Odonata). IV. Development of the adult compound eyes

The changes in the directions of view of marked larval ommatidia were observed after the emergence of the adult. Those ommatidia that had been present during the first larval instar had the most posterior directions of view in the adult visual field while the newest ommatidia that had not been functional for vision in the aquatic larva contributed to the anterior and dorsal foveas of the aerial adults. The changes in interommatidial angles at emergence are discussed. Contrary to the general trend for interommatidial angles between retained larval ommatidia to decrease at emergence, the interommatidial angles in the larval fovea of aeshnid visual predators increase at emergence. The modifications in an odonate compound eye at emergence are like an exaggeration of the modifications that occur at the moult from one larval instar to the next, except that the newest ommatidia do not have any compromises in their design for use in the aquatic vision of the larvae. This is in contrast to the ommatidia retained from the earliest larval instars which have to have the most compromises in their design so that they can be adapted for the visual requirements of every larval instar, as well as the adult. This is discussed in relation to the trend among advanced species of odonates to replace the larval ommatidia by an entirely new set of adult ommatidia.     

3D maps of RNA interhelical junctions

More than 50% of RNA secondary structure is estimated to be A-form helices, which are linked together by various junctions. Here we describe a protocol for computing three interhelical Euler angles describing the relative orientation of helices across RNA junctions. 5' and 3' helices, H1 and H2, respectively, are assigned based on the junction topology. A reference canonical helix is constructed using an appropriate molecular builder software consisting of two continuous idealized A-form helices (iH1 and iH2) with helix axis oriented along the molecular Z-direction running toward the positive direction from iH1 to iH2. The phosphate groups and the carbon and oxygen atoms of the sugars are used to superimpose helix H1 of a target interhelical junction onto the corresponding iH1 of the reference helix. A copy of iH2 is then superimposed onto the resulting H2 helix to generate iH2'. A rotation matrix R is computed, which rotates iH2' into iH2 and expresses the rotation parameters in terms of three Euler angles α(h), β(h) and γ(h). The angles are processed to resolve a twofold degeneracy and to select an overall rotation around the axis of the reference helix. The three interhelical Euler angles define clockwise rotations around the 5' (-γ(h)) and 3' (α(h)) helices and an interhelical bend angle (β(h)). The angles can be depicted graphically to provide a 'Ramachandran'-type view of RNA global structure that can be used to identify unusual conformations as well as to understand variations due to changes in sequence, junction topology and other parameters.     

Periodic structurally similar oligomers are found on one side of the axes of symmetry in the lac, trp, and gal operators

Three well-defined E. coli operator regions were examined for recurring conformational deviation from a regular B-DNA helix. All three, the lac, trp, and gal, show repeats of the same set of neighboring helical twist angles. These angles recur with a periodicity equal to the helix periodicity on one side of the operator's axes of symmetry. The probability that their occurrence is random was found to be extremely small. Therefore, we propose that in addition to specific bases, repeating twist angles patterns are likely to be among the local parameters involved in repressor-operator recognition.     

Protein structural analysis from solid-state NMR-derived orientational constraints.

High-resolution orientational constraints from solid-state NMR spectroscopy of uniformly aligned biological macromolecules provide a great structural analysis problem. Several approaches to this problem have been made in the past. Here a vector algebra method is developed that provides analytical solutions for the torsion angles and a concise and simple view of the structural possibilities. Numerical instabilities in this approach are easily predicted. Insight into how the structural ambiguities arise in the first place and how they can be reduced in number is demonstrated with this new approach.     

Viewer-centered object representation in the human visual system revealed by viewpoint aftereffects

Are there neurons representing specific views of objects in the human visual system? A visual selective adaptation method was used to address this question. After visual adaptation to an object viewed either 15 or 30 degrees from one side, when the same object was subsequently presented near the frontal view, the perceived viewing directions were biased in a direction opposite to that of the adapted viewpoint. This aftereffect can be obtained with spatially nonoverlapping adapting and test stimuli, and it depends on the global representation of the adapting stimuli. Viewpoint aftereffects were found within, but not across, categories of objects tested (faces, cars, wire-like objects). The magnitude of this aftereffect depends on the angular difference between the adapting and test viewing angles and grows with increasing duration of adaptation. These results support the existence of object-selective neurons tuned to specific viewing angles in the human visual system.     

Orientation and dynamics of transmembrane peptides: the power of simple models

In this review we discuss recent insights obtained from well-characterized model systems into the factors that determine the orientation and tilt angles of transmembrane peptides in lipid bilayers. We will compare tilt angles of synthetic peptides with those of natural peptides and proteins, and we will discuss how tilt can be modulated by hydrophobic mismatch between the thickness of the bilayer and the length of the membrane spanning part of the peptide or protein. In particular, we will focus on results obtained on tryptophan-flanked model peptides (WALP peptides) as a case study to illustrate possible consequences of hydrophobic mismatch in molecular detail and to highlight the importance of peptide dynamics for the experimental determination of tilt angles. We will conclude with discussing some future prospects and challenges concerning the use of simple peptide/lipid model systems as a tool to understand membrane structure and function.     

Investigation of the visual cytoscreening of conventional gynecologic smears. II. Analysis of eye movement

The perception of visual information in cytoscreening was studied: eye movements were recorded while the cytotechnologist was screening cervical smears by means of a projection screen. Four phases of eye movement could be distinguished: small, aimless movements during the stage movement; a latency period with a duration of about 180 milliseconds; saccadic movement to the position of an object; and fixation on an object. These components explain the two-phase behavior of cytoscreening found in our previous investigations of the stage movement. Visual perception during the period of latency was found to be the most important since only those objects that are recognized by peripheral vision during this period can trigger the necessary saccadic movement before fixation takes place. The scanpath of search in the stationary field of view is determined by the conspicuousness of the objects; the main features of conspicuousness are size and contrast. Even with the comparatively small fields of view (24 degrees and 29 degrees in diameter) used in these experiments, it was found that the detection threshold of peripheral vision increases towards the margin of the field of view. This raises the question of whether the use of large-field binoculars (with 40-degree visual angles) may cause higher false-negative rates for samples with only a few atypical cells.     

Determining the three-dimensional relation between the skeletal elements of the human shoulder complex

In this paper, we present an inverse kinematics method to determining human shoulder joint motion coupling relationship based on experimental data in the literature. This work focuses on transferring Euler-angle-based coupling equations into a relationship based on the Denavit–Hartenberg (DH) method. We use analytical inverse kinematics to achieve the transferring. For a specific posture, we can choose points on clavicle, scapula, and humerus and represent the end-effector positions based on Euler angles or DH method. For both Euler and DH systems, the end-effectors have the same Cartesian positions. Solving these equations related to end-effector positions yields DH joint angles for that posture. The new joint motion coupling relationship is obtained by polynomial and cosine fitting of the DH joint angles for all different postures.     

植物花药开裂的细胞学和分子生物学机制

植物花药开裂具有重要的生物学意义,花药开裂异常所导致的最直接后果为花粉粒不能正常散粉,影响到植物受精过程。现从细胞和分子生物学角度综述了植物花药开裂过程中花药组织的细胞结构和生理变化及调控花药开裂相关基因的分离和克隆。     

Solar-absorber antireflector on the eye of an Eocene fly (45 Ma)

Antireflection structures on eyes potentially increase visual efficiency through increased photon capture for a given stimulus condition. We report an unusual surface grating on the compound eyes of an Eocene dolichopodid dipteran (45 Ma) known only from Baltic amber. By measuring the reflective properties of a flat model of this grating constructed from material of appropriate refractive index we show that this ''fly eye grating'' is an efficient antireflector of white light at angles up to 60 degrees, and a relatively good antireflector for angles beyond 60 degrees. We calculate that such a grating would be particularly useful on a curved corneal surface as it would increase the transmission of incident light through the cornea compared with a smooth surface. This structure is also reported on the curved regions of the corneas of at least two extant dipterans. We argue that this grating probably derives from the previously described moth eye antireflection structure, which we also report here to occur in a silverfish, a ''primitive'' insect. The fly eye grating is a more efficient antireflector than the moth eye structure only at angles greater than about 10 degrees from the surface normal. A comparable antireflector is employed on solar absorbers.     

Convergent evolution of domain architectures (is rare)

MOTIVATION: In this paper, we shall examine the evolution of domain architectures across 62 genomes of known phylogeny including all kingdoms of life. We look in particular at the possibility of convergent evolution, with a view to determining the extent to which the architectures observed in the genomes are due to functional necessity or evolutionary descent. We used domains of known structure, because from this and other information we know their evolutionary relationships. We use a range of methods including phylogenetic grouping, sequence similarity/alignment, mutation rates and comparative genomics to approach this difficult problem from several angles. RESULTS: Although we do not claim an exhaustive analysis, we conclude that between 0.4 and 4% of sequences are involved in convergent evolution of domain architectures, and expect the actual number to be close to the lower bound. We also made two incidental observations, albeit on a small sample: the events leading to convergent evolution appear to be random with no functional or structural preferences, and changes in the number of tandem repeat domains occur more readily than changes which alter the domain composition. CONCLUSION: The principal conclusion is that the observed domain architectures of the sequences in the genomes are driven by evolutionary descent rather than functional necessity. CONTACT: gough@supfam.org.     

Symmetry perception by poultry chicks and its implications for three-dimensional object recognition

Bilateral symmetry is visually salient to diverse animals including birds, but whereas experimental studies typically use bilaterally symmetrical two-dimensional patterns that are viewed approximately fronto-parallel; in nature, animals observe three-dimensional objects from all angles. Many animals and plant structures have a plane of bilateral symmetry. Here, we first (experiment I) give evidence that young poultry chicks readily generalize bilateral symmetry as a feature of two-dimensional patterns in fronto-parallel view. We then test the ability of chicks to recognize symmetry in images that would be produced by the transformed view produced by a 40° horizontal combined with a 20° vertical rotation of a pattern on a spherical surface. Experiment II gives evidence that chicks trained to distinguish symmetrical from asymmetrical patterns treat rotated views of symmetrical 'objects' as symmetrical. Experiment III gives evidence that chicks trained to discriminate rotated views of symmetrical 'objects' from asymmetrical patterns generalize to novel symmetrical objects either in fronto-parallel or rotated view. These findings emphasize the importance of bilateral symmetry for three-dimensional object recognition and raise questions about the underlying mechanisms of symmetry perception.     

Diurnal changes in angular sensitivity of crab photoreceptors

Summary The electrophysiological and anatomical consequences of diurnal changes in screening pigment position were investigated in the apposition eye of the portunid crabScylla serrata. Intracellular recordings revealed that the acceptance angles of dark-adapted photoreceptors enlarged up to four-fold at night compared with photoreceptors dark-adapted in the day. Furthermore, while light adaptation at night caused acceptance angles to narrow, dark adaptation in the day caused no significant broadening of angles. These electrophysiological changes correlated with pigment movements in the eye observed both histologically and in the deep pseudopupil. It is found that the distal pigment cells change diurnally so that the field-stop which these cells form in front of the photoreceptors is opened in the night and closed in the day time.One feature of the diurnal rhythm is that it prevents photoreceptor fields of view enlarging when eyes are dark adapted in the day. InScylla, photoreceptor fields of view take tens of minutes to narrow upon exposure of crabs to light at night. By preventing a similar broadening in the day, the diurnal rhythm may enable animals suddenly leaving dark refuges to be pre-adapted to daylight. To a range of species which utilise refuges such a mechanism would be of significant advantage, especially after disturbance by predators.We are grateful to Prof. G.A. Horridge for constant encouragement and to Drs. S.B. Laughlin, M. Wilson, S. Shaw and M.F. Land for helpful advice.     

A simple method to obtain consistent and clinically meaningful pelvic angles from euler angles during gait analysis

Clinical gait analysis usually describes joint kinematics using Euler angles, which depend on the sequence of rotation. Studies have shown that pelvic obliquity angles from the traditional tilt-obliquity-rotation (TOR) Euler angle sequence can deviate considerably from clinical expectations and have suggested that a rotation-obliquity-tilt (ROT) Euler angle sequence be used instead. We propose a simple alternate approach in which clinical joint angles are defined and exactly calculated in terms of Euler angles from any rotation sequence. Equations were derived to calculate clinical pelvic elevation, progression, and lean angles from TOR and ROT Euler angles. For the ROT Euler angles, obliquity was exactly the same as the clinical elevation angle, rotation was similar to the clinical progression angle, and tilt was similar to the clinical lean angle. Greater differences were observed for TOR. These results support previous findings that ROT is preferable to TOR for calculating pelvic Euler angles for clinical interpretation. However, we suggest that exact clinical angles can and should be obtained through a few extra calculations as demonstrated in this technical note.     

Three-dimensional measurement of rearfoot motion during running

Excessive ranges of motion during running have been speculated to be connected to injuries to the lower extremities. Movement of the foot and lower leg has commonly been studied with two-dimensional techniques. However, differences in the alignment of the longitudinal axis of the foot with the camera axis will produce measurement errors for projected angles of the lower extremities. A three-dimensional approach would not have this limitation. The purpose of this study is to present a three-dimensional model for calculation of angles between lower leg and foot, lower leg and ground, and foot and ground, and to compare results from treadmill running derived from this model with results derived from a two-dimensional model for different alignment angles between foot axis and camera axis. A two camera Selspot system was used to obtain three-dimensional information on motion of the studied segments. It was found that several two-dimensional variables measured from a posterior view are very sensitive to the alignment angle between the foot and the camera axis. Some variables change as much as 1 degrees for every 2 degrees of change of the alignment angle. The large influence of rotations other than the measured one in two-dimensional measurements makes advisable the use of a three-dimensional model when studying motion between foot and lower leg during running.     

Is there an alternative to increasing the sample size in microarray studies?

Our answer to the question posed in the title is negative. This intentionally provocative note discusses the issue of sample size in microarray studies from several angles. We suggest that the current view of microarrays as no more than a screening tool be changed and small sample studies no longer be considered appropriate.