Stereometric craniometry

A method is described whereby three-dimensional co-ordinates of points on a cranium can be recorded in terms of azimuth, elevation and radial distance from a selected point. These co-ordinates can be used to create two-dimensional representations of single crania, the differences between many crania or growth stages of individuals or series of individuals. The co-ordinates can be used in more conventional analytic ways in the same way as cartesian co-ordinates.     

Structural analysis of polymers of sickle cell hemoglobin. II. Sickle hemoglobin macrofibers

Sickle cell hemoglobin macrofibers are an important intermediate in the low pH crystallization pathway of deoxygenated hemoglobin S that link the fiber to the crystal. Macrofibers are a class of helical particles differing primarily in their diameters but are related by a common packing of their constituent subunits. We have performed three-dimensional reconstructions of three types of macrofibers. These reconstructions show that macrofibers are composed of rows of Wishner-Love double strands in an arrangement similar to that in the crystal. We have measured the orientation and co-ordinates of double strands in macrofibers using cross-correlation techniques. In this approach, the electron density projections of double strands calculated from the known high-resolution crystal structure are compared with regions along the length of the particles in which the distinct pattern of double strands in c-axis projection may be observed. Contrary to assertions by Makinen & Sigountos (1984), our results unambigously demonstrate that adjacent rows of double strands in macrofibers are oriented in an antiparallel manner, as in the Wishner-Love crystal. Adjacent rows of antiparallel double strands are displaced along the helical axis relative to their co-ordinates in the crystal. Electron density models of macrofibers based on the crystallographic structure of the sickle hemoglobin double strand are in good agreement with the projections of macrofibers observed in electron micrographs. We have studied the structure of a closely related crystallization intermediate, the sickle hemoglobin paracrystal. The arrangement of double strands in paracrystals is similar to that in Wishner-Love crystals, except that they are displaced along the a-axis of the crystal. Measurements of the double strand co-ordinates reveal that the distribution of strand positions is bimodal. These results further establish the close structural relationship between macrofibers and paracrystals as intermediates in the crystallization of deoxygenated sickle hemoglobin.     

Feasibility of using orthogonal fluoroscopic images to measure in vivo joint kinematics

Accurately determining in vivo knee kinematics is still a challenge in biomedical engineering. This paper presents an imaging technique using two orthogonal images to measure 6 degree-of-freedom (DOF) knee kinematics during weight-bearing flexion. Using this technique, orthogonal images of the knee were captured using a 3-D fluoroscope at different flexion angles during weight-bearing flexion. The two orthogonal images uniquely characterized the knee position at the specific flexion angle. A virtual fluoroscope was then created in solid modeling software and was used to reproduce the relative positions of the orthogonal images and X-ray sources of the 3-D fluoroscope during the actual imaging procedure. Two virtual cameras in the software were used to represent the X-ray sources. The 3-D computer model of the knee was then introduced into the virtual fluoroscope and was projected onto the orthogonal images by the two virtual cameras. By matching the projections of the knee model to the orthogonal images of the knee obtained during weight-bearing flexion, the knee kinematics in 6 DOF were determined. Using regularly shaped objects with known positions and orientations, this technique was shown to have an accuracy of 0.1 mm and 0.1 deg in determining the positions and orientations of the objects, respectively.     

3-D localization of cardiac structures in real time]

Radiographic 3-D localisation enables measurements to be made that facilitate the placement of the interventional device during cardiac intervention. To enable the reader to implement the method himself, we describe the computation of 3-D coordinates, acquisition of the imaging and projection data on-line, and the accuracy that can be expected with the method. The 3-D coordinates of a cardiac structure are calculated from the image point coordinates, the projection data and the system constants of a biplane isocentric X-ray unit. Technical imaging errors are corrected a priori. The biplane projection data of a run are acquired on-line and stored in a data base. The image pair of interest is identified automatically from the inscribed run number, and assigned to the projection data from the data base. The target image point is marked on the monitor for 3-D localisation. The accuracy of the method was determined by comparing the calculated and actual cross-sectional points of a centimetre grid imaged in biplane X-ray projections. 3-D localisation took an average of 9.8 +/- 1.2 seconds. Angles and distances were assessed with a standard error of 1.1 degrees and 0.8 mm. The run number is identified correctly in 98.5% of the cases. The mean absolute location error for all points and image pairs was 0.61 +/- 0.32 mm. The accuracy and precision was 0.03 +/- 0.40 mm. Radiographic 3-D localisation can be performed readily and accurately on-line. The results obtained with the method enable interventional decisions to be optimized.     

High-resolution cryo-electron microscopy on macromolecular complexes and cell organelles

Cryo-electron microscopy techniques and computational 3-D reconstruction of macromolecular assemblies are tightly linked tools in modern structural biology. This symbiosis has produced vast amounts of detailed information on the structure and function of biological macromolecules. Typically, one of two fundamentally different strategies is used depending on the specimens and their environment. A: 3-D reconstruction based on repetitive and structurally identical unit cells that allow for averaging, and B: tomographic 3-D reconstructions where tilt-series between approximately ±60 and ±70° at small angular increments are collected from highly complex and flexible structures that are beyond averaging procedures, at least during the first round of 3-D reconstruction. Strategies of group A are averaging-based procedures and collect large number of 2-D projections at different angles that are computationally aligned, averaged together, and back-projected in 3-D space to reach a most complete 3-D dataset with high resolution, today often down to atomic detail. Evidently, success relies on structurally repetitive particles and an aligning procedure that unambiguously determines the angular relationship of all 2-D projections with respect to each other. The alignment procedure of small particles may rely on their packing into a regular array such as a 2-D crystal, an icosahedral (viral) particle, or a helical assembly. Critically important for cryo-methods, each particle will only be exposed once to the electron beam, making these procedures optimal for highest-resolution studies where beam-induced damage is a significant concern. In contrast, tomographic 3-D reconstruction procedures (group B) do not rely on averaging, but collect an entire dataset from the very same structure of interest. Data acquisition requires collecting a large series of tilted projections at angular increments of 1–2° or less and a tilt range of ±60° or more. Accordingly, tomographic data collection exposes its specimens to a large electron dose, which is particularly problematic for frozen-hydrated samples. Currently, cryo-electron tomography is a rapidly emerging technology, on one end driven by the newest developments of hardware such as super-stabile microscopy stages as well as the latest generation of direct electron detectors and cameras. On the other end, success also strongly depends on new software developments on all kinds of fronts such as tilt-series alignment and back-projection procedures that are all adapted to the very low-dose and therefore very noisy primary data. Here, we will review the status quo of cryo-electron microscopy and discuss the future of cellular cryo-electron tomography from data collection to data analysis, CTF-correction of tilt-series, post-tomographic sub-volume averaging, and 3-D particle classification. We will also discuss the pros and cons of plunge freezing of cellular specimens to vitrified sectioning procedures and their suitability for post-tomographic volume averaging despite multiple artifacts that may distort specimens to some degree.     

Accelerated Optical Projection Tomography Applied to In Vivo Imaging of Zebrafish

Optical projection tomography (OPT) provides a non-invasive 3-D imaging modality that can be applied to longitudinal studies of live disease models, including in zebrafish. Current limitations include the requirement of a minimum number of angular projections for reconstruction of reasonable OPT images using filtered back projection (FBP), which is typically several hundred, leading to acquisition times of several minutes. It is highly desirable to decrease the number of required angular projections to decrease both the total acquisition time and the light dose to the sample. This is particularly important to enable longitudinal studies, which involve measurements of the same fish at different time points. In this work, we demonstrate that the use of an iterative algorithm to reconstruct sparsely sampled OPT data sets can provide useful 3-D images with 50 or fewer projections, thereby significantly decreasing the minimum acquisition time and light dose while maintaining image quality. A transgenic zebrafish embryo with fluorescent labelling of the vasculature was imaged to acquire densely sampled (800 projections) and under-sampled data sets of transmitted and fluorescence projection images. The under-sampled OPT data sets were reconstructed using an iterative total variation-based image reconstruction algorithm and compared against FBP reconstructions of the densely sampled data sets. To illustrate the potential for quantitative analysis following rapid OPT data acquisition, a Hessian-based method was applied to automatically segment the reconstructed images to select the vasculature network. Results showed that 3-D images of the zebrafish embryo and its vasculature of sufficient visual quality for quantitative analysis can be reconstructed using the iterative algorithm from only 32 projections—achieving up to 28 times improvement in imaging speed and leading to total acquisition times of a few seconds.     

Investigation of a New Electrode Array Technology for a Central Auditory Prosthesis

Ongoing clinical studies on patients recently implanted with the auditory midbrain implant (AMI) into the inferior colliculus (IC) for hearing restoration have shown that these patients do not achieve performance levels comparable to cochlear implant patients. The AMI consists of a single-shank array (20 electrodes) for stimulation along the tonotopic axis of the IC. Recent findings suggest that one major limitation in AMI performance is the inability to sufficiently activate neurons across the three-dimensional (3-D) IC. Unfortunately, there are no currently available 3-D array technologies that can be used for clinical applications. More recently, there has been a new initiative by the European Commission to fund and develop 3-D chronic electrode arrays for science and clinical applications through the NeuroProbes project that can overcome the bulkiness and limited 3-D configurations of currently available array technologies. As part of the NeuroProbes initiative, we investigated whether their new array technology could be potentially used for future AMI patients. Since the NeuroProbes technology had not yet been tested for electrical stimulation in an in vivo animal preparation, we performed experiments in ketamine-anesthetized guinea pigs in which we inserted and stimulated a NeuroProbes array within the IC and recorded the corresponding neural activation within the auditory cortex. We used 2-D arrays for this initial feasibility study since they were already available and were sufficient to access the IC and also demonstrate effective activation of the central auditory system. Based on these encouraging results and the ability to develop customized 3-D arrays with the NeuroProbes technology, we can further investigate different stimulation patterns across the ICC to improve AMI performance.     

Unified 3-D structure and projection orientation refinement using quasi-Newton algorithm

We describe an algorithm for simultaneous refinement of a three-dimensional (3-D) density map and of the orientation parameters of two-dimensional (2-D) projections that are used to reconstruct this map. The application is in electron microscopy, where the 3-D structure of a protein has to be determined from a set of 2-D projections collected at random but initially unknown angles. The design of the algorithm is based on the assumption that initial low resolution approximation of the density map and reasonable guesses for orientation parameters are available. Thus, the algorithm is applicable in final stages of the structure refinement, when the quality of the results is of main concern. We define the objective function to be minimized in real space and solve the resulting nonlinear optimization problem using a Quasi-Newton algorithm. We calculate analytical derivatives with respect to density distribution and the finite difference approximations of derivatives with respect to orientation parameters. We demonstrate that calculation of derivatives is robust with respect to noise in the data. This is due to the fact that noise is annihilated by the back-projection operations. Our algorithm is distinguished from other orientation refinement methods (i) by the simultaneous update of the density map and orientation parameters resulting in a highly efficient computational scheme and (ii) by the high quality of the results produced by a direct minimization of the discrepancy between the 2-D data and the projected views of the reconstructed 3-D structure. We demonstrate the speed and accuracy of our method by using simulated data.     

Stress-shielding induced bone remodeling in cementless shoulder resurfacing arthroplasty: a finite element analysis and in vivo results

Cementless surface replacement arthroplasty (CSRA) of the shoulder was designed to preserve the individual anatomy and humeral bone stock. A matter of concern in resurfacing implants remains the stress shielding and bone remodeling processes. The bone remodeling processes of two different CSRA fixation designs, conical-crown (Epoca RH) and central-stem (Copeland), were studied by three-dimensional (3-D) finite element analysis (FEA) as well as evaluation of contact radiographs from human CSRA retrievals. FEA included one native humerus model with a normal and one with a reduced bone stock quality. Compressive strains were evaluated before and after virtual CSRA implantation and the results were then compared to the bone remodeling and stress-shielding pattern of eight human CSRA retrievals (Epoca RH n=4 and Copeland n=4). FEA revealed for both bone stock models increased compressive strains at the stem and outer implant rim for both CSRA designs indicating an increased bone formation at those locations. Unloading of the bone was seen for both designs under the central implant shell (conical-crown 50–85%, central-stem 31–93%) indicating high bone resorption. Those effects appeared more pronounced for the reduced than for the normal bone stock model. The assumptions of the FEA were confirmed in the CSRA retrieval analysis which showed bone apposition at the outer implant rim and stems with highly reduced bone stock below the central implant shell. Overall, clear signs of stress shielding were observed for both CSRAs designs in the in vitro FEA and human retrieval analysis. Especially in the central part of both implant designs the bone stock was highly resorbed. The impact of these bone remodeling processes on the clinical outcome as well as long-term stability requires further evaluation.     

Interactive computer surface graphic study of the binding of an antibody to the chromatin subunit

The binding of an IgG molecule to a chromatin subunit has been simulated by the interactive computer surface graphics technique. This technique permits the facile display of the surface of macromolecules for which atomic co-ordinates are known. The computer generated projections reveal spatial relationship between the IgG and the nucleosome. Studies of these projections provide insights into the immunogenicity and antigenicity of the chromatin subunit. The concepts discussed are helpful in understanding the manner in which IgG molecules specific to DNA bases, chromosomal proteins, irradiated DNA and to chemical carcinogens bind to the genome.     

The three-dimensional structure of human erythrocyte aquaporin CHIP.

Water-permeable membranes of several plant and mammalian tissues contain specific water channel proteins, the 'aquaporins'. The best characterized aquaporin is CHIP, a 28 kDa red blood cell channel-forming integral protein. Isolated CHIP and Escherichia coli lipids may be assembled into 2-D crystals for structural analyses. Here we present (i) a structural characterization of the solubilized CHIP oligomers, (ii) projections of CHIP arrays after negative staining or metal-shadowing, and (iii) the 3-D structure at 1.6 nm resolution. Negatively stained CHIP oligomers exhibited a side length of 6.9 nm with four-fold symmetry, and a mass of 202 +/- 3 kDa determined by scanning transmission electron microscopy. Reconstituted into lipid bilayers, CHIP formed 2-D square lattices with unit cell dimensions a = b = 9.6 nm and a p422(1) symmetry. The 3-D map revealed that CHIP tetramers contain central stain-filled depressions about the fourfold axis. These cavities extend from both sides into the transbilayer domain of the molecule leaving only a thin barrier to be penetrated by the water pores. Although CHIP monomers behave as independent pores, we propose that their particular structure requires tetramerization for stable integration into the bilayer.     

Binding affinity prediction of novel estrogen receptor ligands using receptor-based 3-D QSAR methods

We have recently reported the development of a 3-D QSAR model for estrogen receptor ligands showing a significant correlation between calculated molecular interaction fields and experimentally measured binding affinity. The ligand alignment obtained from docking simulations was taken as basis for a comparative field analysis applying the GRID/GOLPE program. Using the interaction field derived with a water probe and applying the smart region definition (SRD) variable selection procedure, a significant and robust model was obtained (q²_LOO=0.921, SDEP=0.345). To further analyze the robustness and the predictivity of the established model several recently developed estrogen receptor ligands were selected as external test set. An excellent agreement between predicted and experimental binding data was obtained indicated by an external SDEP of 0.531. Two other traditionally used prediction techniques were applied in order to check the performance of the receptor-based 3-D QSAR procedure. The interaction energies calculated on the basis of receptor–ligand complexes were correlated with experimentally observed affinities. Also ligand-based 3-D QSAR models were generated using program FlexS. The interaction energy-based model, as well as the ligand-based 3-D QSAR models yielded models with lower predictivity. The comparison with the interaction energy-based model and with the ligand-based 3-D QSAR models, respectively, indicates that the combination of receptor-based and 3-D QSAR methods is able to improve the quality of prediction.     

A simple non invasive computerized method for the assessment of bone repair within osteoconductive porous bioceramic grafts

Single energy X-ray imaging, due to its low cost and flexibility, is one of the most used and common technique to assess bone state and bone remodeling over time. Standardized X-ray images are needed to compare sets of radiographs for semi-quantitative analyses of tissue remodeling. However, useful mathematical modeling for the analysis of high level radiographic images are not easily available. In order to propose a useful evaluation tool to a wide clinical scenario, we present an innovative calibration algorithm for a semi-quantitative analysis of non-standardized digitized X-ray images. For calibration on a unique standardization scale, three time invariant regions (ROI) of radiographs were selected and analyzed. The accuracy of the normalization method for X-ray films was successfully validated by using an aluminum step wedge for routine X-ray exposures as tool to standardize serial radiographs (Pearson correlation test: R(2) = 0.96). This method was applied to investigate the progression of the new bone deposition within ceramic scaffolds used as osteoconductive substitute in large bone defects taking advantage of a large animal model. This innovative image-processing algorithm allowed the identification and semi-quantification of the bone matrix deposited within the implant. The osteo-integration at the bone-implant interface was also investigated. A progressively increasing bone tissue deposition within the porous bioceramic implant and a progressive osteo-integration was observed during the 12 months of the trial.     

The Arabidopsis thaliana 2-D gel mitochondrial proteome: Refining the value of reference maps for assessing protein abundance, contaminants and post-translational modifications

Mitochondria undertake the process of oxidative phosphorylation yielding ATP for plant cell maintenance and growth. The principles of isolation and fractionation of plant mitochondrial proteins have been improved over decades, and surveys of the mitochondrial proteome in a number of plants species have been performed. Over time, many quantitative analyses of changes in the plant mitochondrial proteome have been performed by 2-D gel analyses revealing the induction, degradation and modification of mitochondrial proteins in responses to mutation, stress and development. Here, we present a saturating MS analysis of 2-D gel separable protein spots from a typical purification of Arabidopsis mitochondria identifying 264 proteins, alongside an LC-MS/MS survey by non-gel methods identifying 220 proteins. This allowed us to characterise the major mitochondrial proteins that are not observed on 2-D gels, the common contaminants and the abundance of the protein machinery of key mitochondrial biochemical pathways, and consider the impact of N-terminal pre-sequence cleavage and phosphorylation as explanations of multiple protein spots and the co-ordinates of proteins on 2-D gels.     

Application of the automated interpretation of electron density maps to Bence-Jones protein Rhe

The automated system for interpreting electron density maps of proteins has been applied to a newly calculated map of Bence-Jones protein Rhe. In order to test the methods and criteria incorporated in the program system, interpretation of Rhe was performed independently of the interpretation by Wang et al. (1974, 1975a,b²), who have used classical Richards box techniques. The automated system produced a single polypeptide chain which accounts for the whole molecule. Much of the secondary structure is detected and atomic co-ordinates are built for most of the main-chain atoms. The results indicate that the program system is able to interpret and build provisional main-chain co-ordinates for an electron density map of reasonable quality.     

A three-dimensional method for calculating currents induced in bodies by extremely low-frequency electric fields

A user-friendly, numerical program has been developed to permit the calculation of induced currents in modeled bodies of human and infrahuman subjects. The program is based on a charge-simulation method (CSM), and it takes into account the three-dimensional (3-D) character of the extremely-low-frequency (ELF) electric field and of the models to be exposed. The principle of the method is to simulate a 3-D object, for example, an animal model, by a combination of several parts (blocks) having simple geometric forms such as a sphere, a cylinder, or a cone. This approach permits easy preparation of input data on the dimensions of the blocks and their positions in a 3-D arrangement. Other input data, such as the coordinates of the contour points and the imaginary values of charges inside objects, which are necessary in the calculations by CSM, are produced automatically by selecting an appropriate "level" for each block, according to its importance. To simulate parts having irregular shapes, special blocks may be added. In one series of experiments, induced currents were calculated for a baboon model in various postures: standing upright, positioned on four legs, and sitting on the floor. Calculated currents, the total induced current in particular, agreed very well with experimental values. Local currents in parts of the baboon models were more variable, ranging from 5% to 17% of measured values in the case of induced currents in the head. Some problems with this method, such as the effect of the dimensions of blocks or the choice of block levels, are discussed.     

Electron Tomography of Single Ice-Embedded Macromolecules: Three-Dimensional Alignment and Classification

From 3-D reconstructions of automatically recorded tilt series of ice-embedded macromolecules, several hundred 3-D images of single particles can be extracted. Here we describe correlation-based techniques to align the particles with respect to translation and orientation in 3-D and the calculation of an averaged reconstruction after application of the correct weighting function to the particle projections. Multivariate statistical analysis and classification are applied to the set of three-dimensionally reconstructed particles to investigate interimage variations on the 3-D level.     

DOMPLOT: a program to generate schematic diagrams of the structural domain organization within proteins, annotated by ligand contacts.

A program is described for automatically generating schematic linear representations of protein chains in terms of their structural domains. The program requires the co-ordinates of the chain, the domain assignment, PROSITE information and a file listing all intermolecular interactions in the protein structure. The output is a PostScript file in which each protein is represented by a set of linked boxes, each box corresponding to all or part of a structural domain. PROSITE motifs and residues involved in ligand interactions are highlighted. The diagrams allow immediate visualization of the domain arrangement within a protein chain, and by providing information on sequence motifs, and metal ion, ligand and DNA binding at the domain level, the program facilitates detection of remote evolutionary relationships between proteins.     

Towards 3-D modelling of epithelia by computer simulation.

The present work is a preliminary step towards dynamic 3-D modelling by computer graphics simulation of the structure of normal and pathological epithelia, using an expert system. In its present state, Esexsy (Epithelium Simulation by EXpert SYstem) allows the construction, through iterative steps, of a simple 3-D representation of the nasal epithelium, based on the positions, sizes and shapes of nuclei. The iterative process is based on statistical comparisons between distributions of parameter values calculated from real (2-D) histological sections and those issued from an equivalent computer 'section' through the simulated 3-D image. We show the results of attempts at simulating normal, metaplastic and dysplastic states of the nasal epithelium, the latter two being characterized by a progressive architectural disorganization, accompanied by nuclear size/shape alterations. The representation takes into account the size, shape, orientation and spatial arrangement of nuclei, with one or several layers from the basal lamina to the lumen. A modified Poisson point process is used at present to position the nuclei, which are modelled by bi-axial spheroids (from prolate to oblate through spherical), with random orientation and size/shape deviations. It should be possible to use the same computer program to simulate other types of epithelia and to achieve increasingly realistic representations by incorporating, notably, nuclear deformations and chromatin texture.     

A variable gap penalty function and feature weights for protein 3-D structure comparisons.

We have developed a variable gap penalty function for use in the comparison program COMPARER which aligns protein sequences on the basis of their 3-D structures. For deletions and insertions, components are a function of structural features of individual amino acid residues (e.g. secondary structure and accessibility). We have also obtained relative weights for different features used in the comparison by examining the equivalent residues in weight matrices and in alignments for pairs of 3-D structures where the equivalencies are relatively unambiguous. We have used the new parameters and the variable gap penalty function in COMPARER to align protein structures in the Brookhaven Data Bank. The variable gap penalty function is useful especially in avoiding gaps in secondary structure elements and the new feature weights give improved alignments. The alignments for both azurins and plastocyanins and N- and C-terminal lobes for aspartic proteinases are discussed.