Three-dimensional Spatial Arrangement Research Articles

Generating a model of the three-dimensional spatial distribution of neurons using density maps

Microcolumns are a vertical arrangement of neocortical neurons that may constitute a fundamental computational ensemble but have been difficult to study morphologically because of the challenges of determining the three-dimensional (3D) spatial arrangements of individual neurons in the ensemble. Previously, a statistical density map method was developed to characterize microcolumns using two-dimensional (2D) coordinates of neurons from thin tissue sections. Here we extend this approach to derive the relationship between these 2D density maps and the actual 3D properties of microcolumns by creating a theoretical 3D model of cortical neurons. In seven steps, we transform a 3D initial arrangement of neurons from a crystalline lattice, with distances and neuron numbers approximating the idealized cortical microcolumn as assayed by our 2D density map analysis, into a model whose neuronal locations represent a plausible 3D arrangement of neurons in the brain. Because we constrain the transformations on the 3D model by the 2D density map properties, the transformed 3D model will exhibit properties that are consistent with experimental findings regarding microcolumnar anatomy in the brain. Moreover, because our methodology only requires the x,y locations of neurons from thin sections, it is readily accessible to any set of input data regardless of preparation or staining, from human or animals. By generating 3D model neuronal arrangements and comparing between control, aged, and diseased brain, our method can be used to test hypotheses about the effects of neurological diseases as well as normal aging on the 3D structure of microcolumns in the brain.

Technique to study three-dimensional spatial arrangement of synaptic vesicles using data from single sections.

Synaptic vesicles are membrane-bound organelles storing neurotransmitters in presynaptic terminals and releasing them into the synaptic cleft. Coordinated movements of synaptic vesicles relate to synaptic function and their spatial arrangement can provide useful information about the activity of a synapse. This article presents a technique to extract quantitative information about three-dimensional (3D) spatial arrangement of synaptic vesicles from measurements performed on single ultrathin random sections of a presynaptic terminal. The technique presumes quantification of a 2D density as well as 2D spatial pattern formed by vesicle profiles using a minimum spanning tree (MST) algorithm, in digitized micrographs of a presynaptic terminal. Further, original software was used to simulate a 3D spatial arrangement of synaptic vesicles and their random sectioning. A 3D density and pattern of synaptic vesicles were used as basic input parameters of the model, while a 2D density and MST quantities for vesicle profiles served as output, model-derived parameters allowing one to compare and fit simulated distributions to experimental ones. Pilot simulations performed to check the validity of the technique have shown that a 2D density and MST quantities of vesicle profiles closely relate to a 3D density and spatial pattern of vesicles. The technique was demonstrated in the analysis of spatial distribution of synaptic vesicles in axonal terminals forming asymmetric synaptic densities in the stratum radiatum of the CA1 subfield of the murine hippocampus.

Computer simulations of particle strengthening: the effects of dislocation dissociation on lattice mismatch strengthening

Precipitation hardening is investigated by simulating the dislocation glide through obstacle fields and determining the critical resolved shear stress. Lattice mismatch strengthened materials are considered (e.g. Cu-rich Cu–Co alloys). The precipitates are spherical; the distribution of their radii and their three-dimensional spatial arrangement are close to those of an actual Ostwald-ripened crystal. The basic simulation approach is the same one as in [V. Mohles, in press]. Unlike in [V. Mohles, in press], the dislocation dissociation into Shockley partials is taken into account; two dislocations with Burgers vectors of the type ( a/6) 〈112〉 are simulated, where a is the lattice constant. The elastic interaction of each of them with itself and with the other one is fully allowed for. This interaction concept is basically identical with that introduced by Brown [L.M. Brown, Phil. Mag. 10 (1964) 441] and Bacon [D.J. Bacon, Phys. Stat. Sol. 23 (1967) 527]. The mean particle radius r ̄ is varied within the range 0.5≤ r ̄ ≤16 nm. Both cases r ̄ < d and r ̄ > d are covered by this range where d is the eqilibrium distance between the Shockley partials of a dissociated dislocation in a Cu-matrix.

Orowan process controlled dislocation glide in materials containing incoherent particles

Dislocation glide in a matrix containing incoherent spherical particles is simulated on a computer. The critical resolved shear stress (CRSS) is derived. The simulations are based on the local stress equilibrium along the dislocation line. The stress terms taken into account are the external applied stress, a viscous drag stress, the obstacle stress and the dislocation self-stress. The latter stress term is similar to the approaches of Brown [Phil. Mag. 10 (1964) 441] and Bacon [Phys. Stat. Sol. 23 (1967) 527]; it replaces the line tension model and fully allows for the elastic interaction of a dislocation with itself and with other dislocations. The particles have a radii distribution and a three-dimensional spatial arrangement, both of which are close to those of an actual crystal. The CRSS is calculated as a function of the mean particle radius and of the particle volume fraction. This function is compared with a recent theoretical one. If a minor correction to this latter function is permitted, it represents the present simulation results well.

Simulations of dislocation glide in overaged precipitation-hardened crystals

Abstract Precipitation hardening of metals and alloys is investigated by means of computer simulations of dislocations gliding through a matrix with spherical coherent precipitates. The critical resolved shear stress is derived. Most realistic models are applied in these simulations: the radius distribution and the three-dimensional spatial arrangement of the particles are close to those of an actual Ostwald ripened crystal. Unlike the surrounding matrix, the precipitates are long-range ordered. A dislocation cutting through them generates an antiphase boundary and hence senses an obstacle stress inside the precipitates, which impedes dislocation glide. Such a strengthening mechanism is effective for instance in the nickel-based superalloy Nimonic PE16. The simulations are based on the local stress equilibrium along the dislocation line. The linear elastic interaction of the dislocations with themselves and with other dislocations is fully allowed for, similar to the approaches of Brown and of Bacon. Overaged crystals are considered in which dislocation glide is governed by the Orowan process. The average particle radius r and the particle volume fraction ƒ are varied. The strengthening contribution of these particles is derived as a function of the parameters r and f. This function is compared with a recent theoretical function suggested by Nembach; after adding a minor correction term to the latter function, it represents the present simulation results well.

Probing protein surface topology by chemical surface labeling, crosslinking, and mass spectrometry.

The higher order structural properties of peptides and proteins are commonly investigated in the solid state by X-ray diffraction crystallography (1) or in solution by multidimensional nuclear magnetic resonance (NMR) spectroscopy (2). These techniques can provide detailed structural information; however, they are severely limited by the quantity of protein required for the analyses, difficulties with crystallization of certain proteins (e.g., glycoproteins), and the poor solubility of many macromolecules. Moreover, these methods are generally time consuming and tedious. Computer-based molecular modeling offers an alternative method to obtain information on the three-dimensional spatial arrangement of a protein. The success of this approach, however, is dependent on prior knowledge of the tertiary structure of an homologous protein (3–5). Due to these limitations, there is an increasing demand for an independent method to probe protein structure and/or confirm information obtained by the techniques mentioned above.

Variations in three-dimensional cancellous bone architecture of the proximal femur in female hip fractures and in controls.

Cubes of cancellous bone were obtained from proximal femora of women with hip fractures (n = 26) and from female cadaveric controls (n = 32) to compare architecture and mechanics between groups. Specimens were scanned on a microcomputed tomography system. Stereologic algorithms and model-based estimates were applied to the data to characterize the three-dimensional cancellous microstructure. Cubes were mechanically tested to failure to obtain mechanical properties. Specimens from control subjects had significantly higher bone volume fraction, trabecular number, and connectivity than specimens from patients with hip fractures; no difference in trabecular thickness was observed between groups. Both maximum modulus and ultimate stress were significantly higher in the control than in the fracture group, consistent with the higher bone volume found in the control group. No statistical differences in any of these architectural or mechanical variables were found when groups were matched for bone volume. Specimens from both patients with hip fractures and controls demonstrated strong relationships between trabecular number and bone volume fraction that were statistically equivalent, suggesting that for a given bone mass, both groups have the same overall number of trabeculae. However, there was an architectural difference between fracture and control groups in terms of the three-dimensional spatial arrangement of trabeculae. Fracture specimens had a significantly more anisotropic (oriented) structure than control specimens, with proportionately fewer trabecular elements transverse to the primary load axis, even when matched for bone volume. Relationships between mechanical and architectural parameters were significantly different between groups, suggesting that fracture and control groups have different structure-mechanics relationships, which we hypothesize may be a consequence of the altered three-dimensional structure between groups.

Small-Angle Neutron Scattering from Anisotropic Single-Crystalline Materials

`Isotropic' small-angle scattering (SAS), i.e. without azimuthal dependence around the primary beam, occurs only for specific configurations of the scattering objects if single-crystalline material is studied. For decomposing Ni-based alloy single crystals, SAS signals are generally highly anisotropic. From analysis of two-dimensional SAS patterns, important information on the evolution of the morphology and on the three-dimensional spatial arrangement of the precipitates from the early stages of decomposition can be extracted. The real-space information obtained from transmission electron microscopy is an excellent complement to the reciprocal-space information extracted from SAS data. The complementary use of these two techniques offers a valuable approach to the study of precipitation phenomena.

Chapter 9 Electron Microscopic Imaging of Chromatin with Nucleosome Resolution

Nuclear DNA in eukaryotes has a nucleosomal organization. Specific assemblies of nucleosomes and nonhistone nuclear proteins play important roles in local transcriptional regulation and in large-scale regulatory events, such as silencing and heterochromatization. The three-dimensional conformation and spatial arrangement of these assemblies plays a crucial functional role, and a complete understanding of nuclear processes must include architectural and compositional aspects. Imaging methods provide reliable information at a level of resolution sufficient to complement and assist in the interpretation of molecular data. There are two principal modes of studying chromatin with conventional transmission electron microscopy, each having advantages and disadvantages. For both, it is important to recognize the various levels of uncertainty that accompany each preparative step and to take this into account in interpreting the final images. In situ studies employ sections of cells or nuclei that are subjected to chemical fixation or cryoimmobilization. These methods preserve intranuclear location and relationships among large-scale nuclear structures.

Computer Simulation of Protein-induced Structural Changes in Closed Circular DNA

The effect of protein-induced wrapping on overall DNA folding is studied using Monte Carlo computer simulation techniques. A new modeling scheme is devised to represent configurations of closed circular DNA containing fragments of the double helix partially wrapped around a core of proteins. The DNA consists of two regions, a fragment wrapped in a left-handed superhelical path around a `phantom' protein core and a free connecting loop. The loop has at least one single-stranded scission so that it can assume a torsionally relaxed state. The configuration of the loop is varied during the course of the computer simulations and the three-dimensional spatial arrangements of lowest total energy are identified. The axis of the DNA loop is represented by a finite three-dimensional Fourier series perturbation of an initial Bezier curve, making it possible to fix the position and orientation of the chain ends as well as the contour length of the free loop. The energy is approximated by elastic terms for the bending and twisting of the DNA and an excluded volume contribution that prevents the self-intersection of sequential distant chain segments. The proportions of the protein-DNA complex, the number of superhelical turns, the chain length and the imposed linking number difference of the closed DNA are varied in the calculations. The resulting minimum energy structures are consistent with physical models and suggest new ways to think about how proteins add and remove supercoils from DNA. Of special note in this regard is the sudden collapse of three-dimensional structure that accompanies small incremental wrapping of the DNA around the idealized protein core. These observations offer new structural insight into the mechanisms of action of proteins which add or remove supercoils from DNA and provide a first step in thinking about the activity of such systems at the chemical level whereby small fluctuations in local molecular structure are translated into large-scale macromolecular changes. The configurations identified in the simulations can also be examined in the context of the well known "linking number paradox" associated with nucleosome formation on closed circular plasmids. The findings bear relevance to DNA with natural curvature as well as to protein-induced bending and deformations of the double helix.

Visual structures for achromatic color perceptions.

Accuracy of achromatic perceptions (correctly seeing blacks, grays, and whites) was investigated for three-dimensional rooms, painted matte black or white, presented empty or containing matte or specular, and black, middle gray, or white objects. The rooms were illuminated by a point source at various locations or by extended sources. Observers judged the achromatic color of four walls in the room, and in one experiment the objects in the room, with wide-angle binocular viewing, or judged the far wall under reduction conditions. At issue were questions about absolute and relative achromatic (lightness) constancy, specification of the proximal stimulus for achromatic perceptions, and the relevance of Gilchrist’s, Land’s, Wallach’s, and Helson’s theoretical concepts. Despite the three-dimensional spatial arrangements and many variations in experimental conditions, achromatic perceptions were tied to ratios of luminances (contrast ratios or CRs) among surfaces. Moreover, the larger the CR’s magnitude, the greater the apparent achromatic difference between surfaces. These achromatic distributions for the perceived colors of the walls were approximately centered on middle gray, when intrasurface luminances were heterogeneous, and on white, when intrasurface luminances were very homogeneous. Despite wide-angle binocular viewing, absolute achromatic constancy occurred only if the CRs were caused by reflectance differences between matte surfaces or within a specular surface. (The stimulus for apparent white could sometimes be an exception to this.) Constancy failed when CRs were caused by illumination gradients on surfaces, even though the scene was three-dimensional and complexly structured. Achromatic constancy depended, therefore, on CRs and on the probability of occurrence of specific physical events. A theory of achromatic perception is described, based on CRs, Helsonian averages, a simple proposition about the illumination, and a concept of nonspatial achromatic segregation.

Single atom sputtering events Direct observation of near-surface depleted zones in ion-irradiated tungsten

Abstract The three-dimensional spatial arrangement of vacancies contained in depleted zones (DZs) of ion-irradiated tungsten specimens, has been determined with atomic resolution by the field-ion microscope (FIM) technique. These DZs were detected in the near-surface region of specimens which had been irradiated in situ at  15 K with 20 keV W+, 30 keV W+, Kr+, Cu+ or Ar+ ions. The values of the ion dose employed were small ( 1013 ions cm−2); therefore, each DZ analysed was the result of the impact of a single projectile ion. At the irradiation temperature ( 15 K) both the self-interstitial atoms and vacancies were immobile, so that the primary state of radiation damage was preserved. The following properties of each DZ were determined : (1) the total number of vacancies; (2) the number of vacancies in the near-surface region; (3) the spatial extent-that is, the dimensions required to determine a volume; (5) the average vacancy concentration associated with the near-surface region; (6) the first-nearest...

An immunologic study of the relationships of non-human primates to man

1. 1. The relationships of twelve non-human primate genera to man were studied using antisera produced against the human serum proteins, albumin, haptoglobin 2-1, ceruloplasmin, transferrin, γM-globulin, γG-globulin, group-specific component and immune globulin, by means of immuno-electrophoresis, immunodiffusion and turbidimetric precipitin tests. 2. 2. Cluster, correlation and principal component analyses revealed an almost constant order of primate relationships for each protein. 3. 3. A computer-drawn, three-dimensional spatial arrangement of the genera yielded family clusters in the sequence Hominidae, Pongidae, Cercopithecidae, Cebidae, Lorisidae and Tupaiidae.