Publications
89 results found
Stark H, Orlova EV, Rinke-Appel J, et al., 1997, Arrangement of tRNAs in pre- and posttranslocational ribosomes revealed by electron cryomicroscopy., Cell, Vol: 88, Pages: 19-28, ISSN: 0092-8674
The three-dimensional structure of the translating 70S E. coli ribosome is presented in its two main conformations: the pretranslocational and the posttranslocational states. Using electron cryomicroscopy and angular reconstitution, structures at 20 A resolution were obtained, which, when compared with our earlier reconstruction of "empty" ribosomes, showed densities corresponding to tRNA molecules--at the P and E sites for posttranslocational ribosomes and at the A and P sites for pretranslocational ribosomes. The P-site tRNA lies directly above the bridge connecting the two ribosomal subunits, with the A-site tRNA fitted snugly against it at an angle of approximately 50 degrees, toward the L7/L12 side of the ribosome. The E-site tRNA appears to lie between the side lobe of the 30S subunit and the L1 protuberance.
van Heel M, Orlova EV, Dube P, et al., 1996, Intrinsic versus imposed curvature in cyclical oligomers: the portal protein of bacteriophage SPP1., EMBO J, Vol: 15, Pages: 4785-4788, ISSN: 0261-4189
Large cyclical oligomers may be formed by (curvi-) linear polymerization of monomers until the n(th) monomer locks in with the first member of the chain. The subunits in incomplete structures exhibit a natural curvature with respect to each other which can be perturbed when the oligomer closes cyclically. Using cryo-electron microscopy and multivariate statistical image processing we report herein a direct structural observation of this effect. A sub-population (approximately 15%) of incomplete oligomers was found within a sample of SPP1 bacteriophage portal proteins embedded in vitreous ice. Whereas the curvature between adjacent subunits of the closed circular 13-fold symmetric oligomer is 27.7 degrees, in these incomplete oligomers the angle is only 25.8 degrees, a value which almost allows for a 14-subunit cyclical arrangement. A simple model for the association of large cyclical oligomers is suggested by our data.
Orlova EV, Serysheva II, van Heel M, et al., 1996, Two structural configurations of the skeletal muscle calcium release channel., Nat Struct Biol, Vol: 3, Pages: 547-552, ISSN: 1072-8368
Here we present the determination of the three-dimensional structure of the skeletal muscle Ca2+-release channel in an open state using electron cryomicroscopy and angular reconstitution. In contrast to our reconstruction of the channel in its closed state, the density map of the channel driven towards its open state, by the presence of Ca2+ and ryanodine, features a central opening in the transmembrane region-the likely passageway for Ca2+ ions from the sarcoplasmic reticulum to the cytosol. The opening of the channel is associated with a 4 degree rotation of its transmembrane region with respect to its cytoplasmic region, and with significant mass translocations within the entire cytoplasmic region of the channel tetramer.
Boettcher C, Stark H, van Heel M, 1996, Stacked bilayer helices: a new structural organization of amphiphilic molecules., Ultramicroscopy, Vol: 62, Pages: 133-139, ISSN: 0304-3991
Intriguing helical fibres can be created by self-assembly of simple chiral amphiphilic molecules. We study the parameters governing this spontaneous self-organization by three-dimensional (3D) electron microscopy of the helical fibres embedded in a vitreous ice-matrix. Different stable helices are generated reproducibly using specific combinations of the control parameters in our system. All fibres with diameters less than 25 nm consist of a narrow stack of compartmented bilayers twisted into a left-handed helix. Our novel helical 3D reconstruction procedures in combination with specialized cryomicroscopical specimen preparation, can rapidly elucidate the structure of such helical assemblies. This approach may complement or even replace existing diffraction-based methodologies.
van Heel M, Harauz G, Orlova EV, et al., 1996, A new generation of the IMAGIC image processing system., J Struct Biol, Vol: 116, Pages: 17-24, ISSN: 1047-8477
One of the aims of modern microscopy is to quantify two-, three-, or even four-dimensional phenomena in biology, medicine, and material sciences. The requirements imposed on software by such data processing are exemplified by the design considerations of the IMAGIC-5 software system. This system includes facilities for multivariate statistical analysis of large data sets, for correlation averaging of two-dimensional crystals, and for three-dimensional reconstruction of macromolecular structures. The molecules may be arranged as two-dimensional crystals, as helices, or as single particles with arbitrary pointgroup symmetry. IMAGIC's novel angular reconstitution approach allows for the rapid determination of three-dimensional structures of uncrystallized molecules to high resolution. The general organization, user interaction strategy, file structure, and extendibility of IMAGIC are discussed and illustrated with some practical examples.
Stark H, Mueller F, Orlova EV, et al., 1995, The 70S Escherichia coli ribosome at 23 A resolution: fitting the ribosomal RNA., Structure, Vol: 3, Pages: 815-821, ISSN: 0969-2126
BACKGROUND: The ribosome--essential for protein synthesis in all organisms--has been an evasive target for structural studies. The best available structures for the 70S Escherichia coli ribosome or its 30S and 50S subunits are based on electron microscopical tilt experiments and are limited in resolution to 28-55 A. The angular reconstitution approach, which exploits the random orientations of particles within a vitreous ice matrix, can be used in conjunction with cryo-electron microscopy to yield a higher-resolution structure. RESULTS: Our 23 A resolution map of the 70S ribosome elucidates many structural details, such as an extensive system of channels within the 50S subunit and an intersubunit gap ideally shaped to accommodate two transfer RNA molecules. The resolution achieved is sufficient to allow the preliminary fitting of double-helical regions of an earlier three-dimensional ribosomal RNA model. CONCLUSIONS: Although we are still a long way from attaining an atomic-resolution structure of the ribosome, cryo-electron microscopy, in combination with angular reconstitution, is likely to yield three-dimensional maps with gradually increasing resolution. As exemplified by our current 23 A reconstruction, these maps will lead to progressive refinement of models of the ribosomal RNA.
Serysheva II, Orlova EV, Chiu W, et al., 1995, Electron cryomicroscopy and angular reconstitution used to visualize the skeletal muscle calcium release channel., Nat Struct Biol, Vol: 2, Pages: 18-24, ISSN: 1072-8368
We exploit the random orientations of ice-embedded molecules imaged in an electron cryomicroscope to determine the three-dimensional structure of the Ca(2+)-release channel from the sarcoplasmic reticulum (SR) in its closed state, without tilting the specimen holder. Our new reconstruction approach includes an exhaustive search of all different characteristic projection images in the micrographs and the assignment of Euler angle orientations to these views. The 30 A map implied reveals a structure in which the transmembrane region exhibits no apparent opening on the SR lumen side. The extended cytoplasmic region has a hollow appearance and consists, in each monomer, of a clamp-shaped and a handle-shaped domain.
Schatz M, Orlova EV, Dube P, et al., 1995, Structure of Lumbricus terrestris hemoglobin at 30 A resolution determined using angular reconstitution., J Struct Biol, Vol: 114, Pages: 28-40, ISSN: 1047-8477
The three-dimensional (3D) structure of the giant hemoglobin of the common earthworm Lumbricus terrestris was determined from cryomicroscopical images of a vitrified molecular solution. From about 5000 molecular images, the best-fit 3D structure was calculated using recently developed analysis techniques. Multivariate statistical analysis data compression and automatic classification were used to find the characteristic projection images of the oligomer. The angular reconstitution approach was then applied to find the Euler angle orientations of these characteristic views. The Lumbricus hemoglobin molecule has an overall D6 (622) point-group symmetry and is found to have a local threefold symmetry axis within the 1/12th subunit. This additional symmetry appears to predict the presence of 36 abcd globin tetramers in the Lumbricus hemoglobin or a total of 144 heme chains for the whole oligomer. A distinct doughnut-shaped structure is elucidated in the center of the molecule. This central subunit, representing around 10% of the protein volume, may consist of non-heme-containing linker chains found generally in giant annelid hemoglobins.
Sines J, Rothnagel R, van Heel M, et al., 1994, Electron cryomicroscopy and digital image processing of lipoprotein(a)., Chem Phys Lipids, Vol: 67-68, Pages: 81-89, ISSN: 0009-3084
Electron cryomicroscopy was used to study the structure of human lipoprotein(a) (Lp(a)), a plasma lipoprotein implicated in cardiovascular disease. An individual Lp(a) particle consists of a neutral lipid core within a shell of phospholipid, cholesterol and glycoprotein. In principle, electron cryomicroscopy images of single particles should contain structural detail attributable to the density differences among these components and the surrounding buffer. We observed such structural detail in images of frozen, hydrated Lp(a) particles. Lp(a) particles appeared to be roughly spherical in shape with an average diameter of 210 A. As is generally true for unstained samples in vitreous ice, imaged with a low electron dose, these images have low contrast with low signal-to-noise ratios. To increase the signal-to-noise ratio, we averaged classes of similar particles. We began with a set of 5813 randomly oriented Lp(a) particles and generated classes using a linear multivariate statistical method, followed by hierarchical ascendant classification. Our initial classification, based on only the first eight eigenvectors, separated particles on the basis of gross size and shape. After a rough reference-free alignment step, a second classification used the finer details in the images. This approach yielded class averages with structural detail only faintly visible in the raw, single images.
Dube P, Tavares P, Lurz R, et al., 1993, The portal protein of bacteriophage SPP1: a DNA pump with 13-fold symmetry., EMBO J, Vol: 12, Pages: 1303-1309, ISSN: 0261-4189
Electron microscopy in combination with image processing is a powerful method for obtaining structural information on non-crystallized biological macromolecules at the 10-50 A resolution level. The processing of noisy microscopical images requires advanced data processing methodologies in which one must carefully avoid the introduction of any form of bias into the data set. Using a novel multivariate statistical approach to the analysis of symmetry, we studied the structure of the bacteriophage SPP1 portal protein oligomer. This portal structure, ubiquitous in icosahedral bacteriophages which package dsDNA, is located at the site of symmetry mismatch between a 5-fold vertex of the icosahedral shell and the 6-fold symmetric (helical) tail. From previous studies such 'head-to-tail connector' structures were generally accepted to be homododecamers assembled in a 12-fold symmetric ring around a central channel. Using a new analysis methodology we have found that the phage SPP1 portal structure exhibits 13-fold cyclical symmetry: a new point group organization for oligomeric proteins. A model for the DNA packaging mechanism by 13-fold symmetric portal protein assemblies is presented which attributes a coherent functional meaning to their unusual symmetry.
van Heel M, 1991, A new family of powerful multivariate statistical sequence analysis techniques., J Mol Biol, Vol: 220, Pages: 877-887, ISSN: 0022-2836
A novel multivariate statistical approach is presented for extracting and exploiting intrinsic information present in our ever-growing sequence data banks. The information extraction from the sequences avoids the pitfalls of intersequence alignment by analyzing secondary invariant functions derived from the sequences in the data bank rather than the sequences themselves. Such typical invariant function is a 20 x 20 histogram of occurrences of amino acid pairs in a given sequence or fragment thereof. To illustrate the potential of the approach an analysis of 10,000 protein sequences from the National Biomedical Research Foundation Protein Identification Resource is presented, whose analysis already reveals great biological detail. For example, zeta-hemoglobin is found to lie close to amphibian and fish chi-hemoglobin which, in turn, is an important clue to the physiological function of this mammalian early embryonic hemoglobin. The multivariate statistical framework presented unifies such apparently unrelated issues as phylogenetic comparisons between a set of sequences and distance matrices between the constituents of the biological sequences. The Multivariate Statistical Sequence Analysis (MSSA) principles can be used for a wide spectrum of sequence analysis problems such as: assignment of family memberships to new sequences, validation of new incoming sequences to be entered into the database, prediction of structure from sequence, discrimination of coding from non-coding DNA regions, and automatic generation of an atlas of protein or DNA sequences. The MSSA techniques represent a self-contained approach to learning continuously and automatically from the growing stream of new sequences. The MSSA approach is particularly likely to play a significant role in major sequencing efforts such as the human genome project.
van Heel M, 1990, Comments on: 'Classification of images of biomolecular assemblies: a study of ribosomes and ribosomal subunits of Escherichia coli'., J Microsc, Vol: 159, Pages: 113-117, ISSN: 0022-2720
In a recent paper Frank et al. (1988; J. Microsc. 150, 99-115) proposed the use of a hybrid clustering technique to sort macromolecular images. In contrast to the claims made in that paper, however, the proposed technique is less sophisticated than the enhanced hierarchical ascendant classification technique proposed by us a few years earlier. The hybrid approach will lead to partitions which are less optimal in terms of minimizing the total intra-class variance for a predetermined number of classes, irrespective of whether the data show distinct clusters or, rather, possess a quasi-continuous intrinsic structure.
Tichelaar W, van Heel M, 1990, Characteristic views of Escherichia coli RNA polymerase core enzyme in the scanning transmission electron microscope., J Struct Biol, Vol: 103, Pages: 180-184, ISSN: 1047-8477
Eight characteristic views of Escherichia coli RNA polymerase core enzyme are presented which were found using multivariate statistical image processing of about 1000 individual molecular images. The data set was obtained from negatively stained specimens with a scanning transmission electron microscope (STEM) operated in dark field mode. The molecular projections were found to a resolution of around 30 A, thus visualizing new structural details of the core enzyme. An approximate twofold axis seems to relate the beta to the beta' subunit as well as both alpha units to each other.
Schatz M, van Heel M, 1990, Invariant classification of molecular views in electron micrographs., Ultramicroscopy, Vol: 32, Pages: 255-264, ISSN: 0304-3991
Biological macromolecules can exhibit many different orientations in electron microscopical preparations. In particular in vitreous-ice-embedded specimens, the number of different views can be high. Existing techniques of analysis require the alignment of the molecular views relative to one or more reference images with cross-correlation ("matched filtering") techniques and are somewhat unsatisfactory because of the high noise level and the large number of different views in such images. We here propose a method in which first rotation-, translation- and mirror-invariant functions are derived from the large set of input images. These functions are subsequently classified automatically using multivariate statistical classification techniques. The different molecular views in the images can therewith be found without bias, provided that a statistically significant number of copies of the views are present in the data set. The basic ideas are exemplified with realistic model data.
Sasaki H, van Heel M, Zeitler E, et al., 1990, Fine structure of mitochondrial helical filaments revealed by computer image analyses., J Electron Microsc (Tokyo), Vol: 39, Pages: 388-395, ISSN: 0022-0744
In order to clarify the fine structure of the helical filaments appearing in the outer compartment of the mitochondria, Sprague-Dawley strain male rats were given 30% ethanol in drinking water for 90 days. The hepatic tissues of these animals were fixed with perfusion of glutaraldehyde via the portal vein followed by immersion in OsO4 and were then routinely processed for preparation of thin sections. Transmission electron micrographs of the sections were used for computer image analyses of the intramitochondrial helical filaments. With the application of the image analysis, it was revealed that the helical filaments show a right-hand rotating helix of 4.3 nm in thickness, 13.2 nm in diameter of the helix, and 15.7 nm in pitch. Also, with the multivariate statistical analysis and classification method of the IMAGIC image processing system, it was suggested in the classified images that the helical filament has substructures of rod-shaped particles of 4.3 nm in diameter. These particles are considered to be connected to each other and forming the helical structure of the filament.
Sass HJ, Büldt G, Beckmann E, et al., 1989, Densely packed beta-structure at the protein-lipid interface of porin is revealed by high-resolution cryo-electron microscopy., J Mol Biol, Vol: 209, Pages: 171-175, ISSN: 0022-2836
Porin is an integral membrane protein that forms channels across the outer membrane of Escherichia coli. Electron microscopic studies of negatively stained two-dimensional porin crystals have shown three stain accumulations per porin trimer, revealing the locations of pores spanning the membrane. In this study, reconstituted porin lattices embedded in glucose were investigated using the low-dose technique on a cryo-electron microscope equipped with a helium-cooled superconducting objective lens. The specimen temperature was maintained at 5 K to yield an improved microscopic and specimen stability. Under these conditions, we obtained for the first time electron diffraction patterns from porin lattices to a resolution of 3.2 A and images showing optical diffraction up to a resolution of 4.9 A. Applying correlation averaging techniques to the digitized micrographs, we were able to reconstruct projected images of the porin trimer to a resolution of up to 3.5 A. In the final projection maps, amplitudes from electron diffraction and phases from these images were combined. The predominant feature is a high-density narrow band (about 6 A in thickness) that delineates the outer perimeter of the trimer. Since the molecule consists of almost exclusively beta-sheet structure, as revealed by spectroscopic data, we conclude that this band is a cylindrical beta-pleated sheet crossing the membrane nearly perpendicularly to its plane. Another intriguing finding is a low-density area (about 70 A2) situated in the centre of the trimer.
Boekema EJ, van Heel M, 1988, Molecular shape of Lumbricus terrestris erythrocruorin studied by electron microscopy and image analysis., Biochim Biophys Acta, Vol: 957, Pages: 370-379, ISSN: 0006-3002
The molecular structure of erythrocruorin (hemoglobin) from Lumbricus terrestris has been studied by electron microscopy of negatively stained particles. Over 1000 molecular projections were selected from a number of electron micrographs and were then classified by multivariate statistical image-processing techniques. The two main groups of top and side views were each subdivided into smaller classes with significantly different features. About half of the top-view projections exhibit perfect hexagonal symmetry at the current resolution of about 2.0 nm, while the other top views lack this symmetry, probably as a result of tilting of the molecules relative to the carbon support film. The side views were separated into two 'families', each associated with the two different stable side-view positions the molecules can take. From these narrow stable side-views, the two families of projections are, again, generated by tilting. The symmetry properties of the three non-tilted projections show that Lumbricus erythrocruorin has a pointgroup D6 (622) symmetry rather than D3 (32).
van Heel M, Harauz G, 1988, Biological macromolecules explored by pattern recognition., Scanning Microsc Suppl, Vol: 2, Pages: 295-301, ISSN: 0892-953X
Electron microscopy represents a very direct method for determining the structure of biological macromolecules, and complements both the well-established technique of X-ray crystallography (c.f. Blundell and Johnson, 1976) and the still in-its-infancy field of structure prediction (Kolata, 1986, Blundell et al., 1987). Our research has involved establishing a precise methodology based on computerised image analysis and pattern recognition to enhance the visibility of statistically significant structural features in electron images of isolated macromolecules. Our newly developed technique of angular reconstitution enables us to orient in three dimensions the commonly occurring projection forms of the macromolecules and thus perform a 3D reconstruction. In this paper, we describe the steps involved in determining the structure of a biological macromolecule by electron microscopy and image analysis, including pattern recognition and three dimensional reconstruction.
Boekema E, van Heel M, Gräber P, 1988, Structure of the ATP-synthase from chloroplasts studied by electron microscopy and image processing., Prog Clin Biol Res, Vol: 273, Pages: 75-80, ISSN: 0361-7742
Harauz G, Boekema E, van Heel M, 1988, Statistical image analysis of electron micrographs of ribosomal subunits., Methods Enzymol, Vol: 164, Pages: 35-49, ISSN: 0076-6879
Borland L, Harauz G, Bahr G, et al., 1988, Packing of the 30 nm chromatin fiber in the human metaphase chromosome., Chromosoma, Vol: 97, Pages: 159-163, ISSN: 0009-5915
The human genetic material is packed hierarchically within the metaphase chromosome: the DNA molecule together with histone proteins form 11 nm diameter nucleosomes, which are then ordered into the 30 nm thick chromatin fiber. Little is known about the packing of this fiber within the chromosome. We have developed a tracking algorithm with which we followed its path within a three-dimensional reconstruction of a human chromosome computed from a series of electron micrographic projections. Fiber segments were seen to form loops of 100-350 nm diameter. Our observations indicate that these loops--which themselves show no preferred orientation--are organised into regions of roughly 200 nm axial extent.
Holzenburg A, Mayer F, Harauz G, et al., 1987, Structure of D-ribulose-l,5-bisphosphate carboxylase/oxygenase from Alcaligenes eutrophyus H16., Nature, Vol: 325, Pages: 730-732, ISSN: 0028-0836
RuBPcase, D-ribulose-1,5-bisphosphate carboxylase/oxygenase (EC4.1.1.39) is the key enzyme of the reductive pentose phosphate cycle. Because of its biological significance, many structural studies on a number of plant and bacterial RuBPCases have been undertaken, including the enzyme isolated from the autotrophic hydrogen-oxidizing bacterium Alcaligenes eutrophus H16 (refs 2-6). Although both the higher plant enzyme and the A. eutrophus enzyme consist of eight large and eight small subunits (L(8)S(8)), no model describing the quaternary structure is generally accepted. Here we present a model for the A. eutrophus RuBPCase derived from X-ray crystallography of three-dimensional (3D) crystals, and electron microscopy and image analysis of two-dimensional (2D) crystals of the enzyme. The X-ray electron density of RuBPCase in the presence of HCO(-)(3), Mg(2+), and the transition state analogue 2-carboxyarabinitol-1,5-bisphosphate (CABP) shows an L(8)S(8) molecule in which the L(4)S(4) half molecules have local 4-fold symmetry (C4). The local 4-fold axes of the two L(4)S(4) halves do not coincide but are shifted by 36 Å and are related by a crystallographic 2-fold axis perpendicular to and between the local 4-fold axes. Electron microscope data of the enzyme without CABP, which can be perfectly modelled using the X-ray densities, do not show this shift and the low-resolution point group of the molecules in the 2D crystals is D4. Both structures are presented.
Van Heel M, 1987, Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction., Ultramicroscopy, Vol: 21, Pages: 111-123, ISSN: 0304-3991
In computerized tomography as well as in most problems of three-dimensional reconstruction from projections, one knows from the experimental set-up the angular relationships between the projections from which the reconstruction is to be calculated. A serious difficulty is encountered when the angles are not known. In this paper, a method of "angular reconstitution" is described, which allows the a posteriori determination of the relative angular orientations of the projections and thus enables the three-dimensional reconstruction of the object to be calculated. For asymmetric objects, a minimum of three projections is required, which should not be related by a tilt around a single rotation axis. The method can be applied to determine the three-dimensional structure of biological macromolecules based on electron micrographs of randomly oriented individual molecules. Angular reconstitution, in combination with multivariate statistical techniques to classify and average the characteristic views of a molecule forms a complete, self-contained methodology for molecular structure analysis by electron microscopy.
Harauz G, Borland L, Bahr GF, et al., 1987, Three-dimensional reconstruction of a human metaphase chromosome from electron micrographs., Chromosoma, Vol: 95, Pages: 366-374, ISSN: 0009-5915
A complete human metaphase chromosome has been reconstructed from a series of electron microscopical projections obtained by tilting the specimen stage at 3 degree intervals from -60 to +60 degrees. The reconstructed structure is about 3.0 microns long, 1.6 micron wide, and 0.8 micron thick. The mass distribution was fairly homogeneous within the chromatids and neither a hollow nor a dense core was observed. The distribution and course of fibers observed are most consistent with a looping model of chromosome structure.
Harauz G, Stoeffler-Meilicke M, van Heel M, 1987, Characteristic views of prokaryotic 50S ribosomal subunits., J Mol Evol, Vol: 26, Pages: 347-357, ISSN: 0022-2844
Multivariate statistical analysis and classification techniques are powerful tools in sorting noisy electron micrographs of single particles according to their principal features, enabling one to form average images with an enhanced signal-to-noise ratio and a better reproducible resolution. We apply this methodology here to determining the characteristic views of the large (50S) ribosomal subunits from the eubacterium Escherichia coli and the archaebacteria Methanococcus vannielii, Sulfolobus solfataricus, and Halobacterium marismortui. Average images were obtained of the subunit in the common crown and kidney projections, but views of the particle in orientations intermediate between these two extremes were also elucidated for all species. These averages show reproducible detail of up to 2.0 nm resolution, thus enabling the visualization and interspecies comparison of many structural features as a first step toward comparing the actual three-dimensional structures. Our results disprove evolutionary lineages recently postulated on the basis of electron microscopical images of ribosomal subunits.
van Heel M, Stöffler-Meilicke M, 1985, Characteristic views of E. coli and B. stearothermophilus 30S ribosomal subunits in the electron microscope., EMBO J, Vol: 4, Pages: 2389-2395, ISSN: 0261-4189
Large sets of electron microscopic images of the 30S ribosomal subunits of Bacillus stearothermophilus (914 molecules) and Escherichia coli (422 molecules) were analysed with image processing techniques. Using computer alignment and a new multivariate statistical classification scheme, three predominant views of the subunit were found for both species. These views, which together account for approximately 90% of the population of images, were determined to a reproducible resolution of up to 1.7 nm, thus elucidating many new structural details. The angular spread of the molecular orientations around the three main stable positions is remarkably small (less than 8 degrees). Some of the current models for the small ribosomal subunit are incompatible with our new results.
van Heel M, 1984, Multivariate statistical classification of noisy images (randomly oriented biological macromolecules)., Ultramicroscopy, Vol: 13, Pages: 165-183, ISSN: 0304-3991
Multivariate Statistical Analysis (MSA) methods have recently been introduced for analyzing images of biological macromolecules [Van Heel and Frank, Ultramicroscopy 6 (1981) 187]. With these techniques, the significant characteristics of each molecular image can be expressed in merely 2 to 8 factorial coordinate values rather than in the typical 64 X 64 = 4096 pixel grey values that originally described the image. This very large reduction in total amount of data facilitates the understanding of the general behavior of a set of molecular images in terms of classes or of general trends in the data set. The (artificial) intelligence of the procedure, however, lies in the decision-making or classification phase. The theory and philosophy of multivariate statistical classification are reviewed using generalized metrics. Problem-dependent classification rationales are proposed. A set of computer-generated "randomly oriented molecular images" are used to test the classification schemes. This model experiment is a step towards 3D structure analysis of macromolecules based on large numbers of (noisy) electron microscopical images of randomly oriented biological macromolecules.
Frank J, van Heel M, 1982, Correspondence analysis of aligned images of biological particles., J Mol Biol, Vol: 161, Pages: 134-137, ISSN: 0022-2836
van Heel M, Frank J, 1981, Use of multivariate statistics in analysing the images of biological macromolecules., Ultramicroscopy, Vol: 6, Pages: 187-194, ISSN: 0304-3991
We have developed a new technique of analysis that allows automatic classification of molecule images according to subtle differences. Computer alignment and multivariate statistical methods were used to analyze electron micrographic images of horseshoe crab hemocyanin half-molecules. The molecule projections fell into four distinct classes related to four different positions of the molecule on the grid. Averages obtained for each images subset are interpreted in terms of a three-dimensional model arrangement for the four subunits forming the half-molecule.
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