Precession electron diffraction: observed and calculated intensities.

Theory and algorithms have been developed for performing kinematical and dynamical two-beam and multibeam dynamical simulations of precession electron diffraction patterns. Intensities in experimental precession patterns have been quantified and are shown to be less dynamical.

Structure determination of the hexagonal quasicrystal approximant micro'-(Al,Si)4Cr by the strong reflections approach.

A number of different crystalline phases have been found in Al-rich Al-Cr-Si alloys by transmission electron microscopy (TEM). Among these, the new hexagonal phase micro'-(Al,Si)(4)Cr (a=2.01 and c=1.24 nm) often found coexisting with the hexagonal micro-(Al,Si)(4)Cr (a=1.998 and c=2.4673 nm, isostructural with micro-Al(4)Mn) and also with the hexagonal lambda-(Al,Si)(4)Cr (a=2.839 and c=1.239 nm, isostructural with lambda-Al(4)Mn). It is evident from their electron diffraction patterns that the structures of these three phases are related. The strong reflections in all three are distributed in a similar way. They all exhibit a pseudo-icosahedral symmetry. The structure factor amplitudes and phases for the strong reflections of the micro' phase could therefore be adopted from those of the lambda phase, according to the strong reflections approach. A structure model of the micro' phase is thus deduced from the known lambda-Al(4)Mn. micro' consists of chains of 3+3 or 4+2 interpenetrated icosahedra along the 100 directions. Similar to the lambda phase, there are two flat layers (F) and four puckered layers (P) in each unit cell of micro', stacked along the c-axis in a sequence of PFP(PFP)' where the (PFP)' block is related to the PFP block by a 6(3) screw.

Structural studies of cytochrome reductase. Subunit topography determined by electron microscopy of membrane crystals of a subcomplex.

Ubiquinol: cytochrome c reductase was isolated from Neurospora mitochondria as a protein-detergent complex and dissociated by mild salt treatment. Three parts were obtained and characterized. Firstly, a complex containing the subunits III (cytochrome b), IV (cytochrome c1), VI, VII, VIII and IX; secondly, a complex containing the subunits I and II; and thirdly, the single subunit V (iron-sulphur subunit). Membrane crystals were prepared from the cytochrome bc1 subunit complex and by combining tilted electron microscopic views of the crystals, a low-resolution three-dimensional structure was calculated. This structure was compared to that of the whole cytochrome reductase (previously determined by electron microscopy of membrane crystals). Protein density absent from the structure of the subunit complex was then attributed to the missing subunits according to their size and shape and their association with the phospholipid bilayer.

Structural studies of cytochrome reductase. Improved membrane crystals of the enzyme complex and crystallization of a subcomplex.

Membrane crystals of mitochondrial ubiquinol: cytochrome c reductase of improved size and long-range order and of the cytochrome bc1 subcomplex have been obtained by a dialysis method. The enzyme--Triton X-100 complex was mixed with Triton phospholipid micelles and the Triton slowly removed by dialysis for 48 hours at pH 5.5 at room temperature or above. The effect of varying the pH and temperature on the shape, size and order of the crystals is described.

Measurement of crystal thickness and crystal tilt from HRTEM images and a way to correct for their effects.

The effects of thickness and tilt angle are studied numerically on experimental high-resolution transmission electron microscope (HRTEM) images of a wedge-shaped metal oxide crystal. For sufficiently thin and well-aligned crystals, the amplitudes and phases of the Fourier transforms of the HRTEM images are essentially the same as the crystallographic structure factors. For tilted crystals, the changes of amplitudes and phases as a function of increased thickness and tilt angle can be described by a simple model. A method is presented by which the local thickness can be determined from one HRTEM image and one convergent-beam electron diffraction pattern from the same crystal. It is also shown how the projected potential can be reconstructed from HRTEM images of tilted crystals, disclosing the crystal structure, even from quite thick (>20 nm) samples.

Structures of nanometre-size crystals determined from selected-area electron diffraction data.

The structure of a new modification of Ti2Se, the beta-phase, and several related inorganic crystal structures containing elements with atomic numbers between 16 and 40 have been solved by quasi-automatic direct methods from single-crystal electron diffraction patterns of nanometre-size crystals, using the kinematical approximation. The crystals were several thousand times smaller than the minimum size required for single-crystal X-ray diffraction. Atomic coordinates were found with an average accuracy of 0.2 A or better. Experimental data were obtained by standardized techniques for recording and quantifying electron diffraction patterns. The SIR97 program for solving crystal structures from three-dimensional X-ray diffraction data by direct methods was modified to work also with two-dimensional electron diffraction data.

Three-dimensional reconstruction of the nu-AlCrFe phase by electron crystallography.

The three-dimensional (3D) structure of the huge quasicrystal approximant nu-AlFeCr (space group P6(3)/m, a = 40.687 and c = 12.546 A) was solved by electron crystallography. High-resolution transmission-electron-microscopy (HREM) images and selected-area electron diffraction patterns from 13 different zone axes were combined to give a 3D potential map. 124 out of 129 unique atoms were found in the 3D map. Procedures for ab initio structure determination by 3D reconstruction are given. It is demonstrated that 3D reconstruction from HREM images is very powerful for solving structures--even very complicated ones. There is no limit in terms of the number of unique atoms in a structure that can be solved by 3D reconstruction.

Structure projection retrieval by image processing of HREM images taken under non-optimum defocus conditions.

A direct method for retrieval of the projected potential from a single HREM image of a thin sample is presented. Both out-of-focus and astigmatic images can be restored. The defocus and astigmatism values are first determined from the Fourier transform of the digitised HREM image. Then a filter is applied which reverts the phases of those Fourier components which have been reversed by the Contrast Transfer Function (CTF). The method has been incorporated into the CRISP image processing system. It can be applied on any sample, crystalline or amorphous. From thin crystalline areas the projected symmetry can be determined and a further improvement achieved by imposing the symmetry exactly. This compensates for the effects of crystal tilt. Five HREM images of a thin crystal of K(8-x)Nb(16-x)W(12+x)O80 (x = 1), taken with different defocus and astigmatism values, were processed. Only one, taken near Scherzer defocus, was directly interpretable before image processing. After processing, all images showed the projected potential of the structure. Using data to 2.77 angstroms resolution, all heavy (Nb/W) atom positions were found in every image, within on average 0.15 angstroms of the positions determined by single crystal X-ray diffraction. In the HREM images taken under non-optimum defocus conditions, also the potassium atoms in the tunnels of the structure were found.

Structure model for the tau(mu) phase in Al-Cr-Si alloys deduced from the lambda phase by the strong-reflections approach.

There are very obvious common features in the electron diffraction patterns of the lambda and tau(mu) phases in the Al-Cr-Si system. The positions of the strong reflections and their intensity distributions are similar for the two structures. The relation of the reciprocal lattices of the lambda and tau(mu) phases is studied. By applying the strong-reflections approach, the structure factors of tau(mu) are deduced from the corresponding structure factors of the known lambda phase. Rules for selecting reflections for the strong-reflections approach are described. Similar to that of lambda, the structure of tau(mu) contains six layers stacked along the c axis in each unit cell. There are 752 atoms in each unit cell, 53 of them are unique. The corresponding composition of the tau(mu) model is Al(3.82 - x)CrSi(x). Simulated electron diffraction patterns from the structure model are in good agreement with the experimental ones. The arrangement of interpenetrated icosahedral clusters in the tau(mu) phase is discussed.

A pentagonal cluster in certain approximants to decagonal quasicrystals.

A certain pentagonal cluster occurring in several approximants to the decagonal quasicrystal is discussed. The term 'cluster' is used here to denote a structure motif which is a certain assemblage of coordination polyhedra. The cluster resembles a wheel with an 'axis' and a 'tyre'. It is built up of seven intergrown icosahedra. The 'wheel cluster' builds up structures of infinite strands or nets perpendicular to the pentagonal wheel cluster axis. The wheel cluster is the main constituent of the decagonal approximant structure types Al3Mn, Al60Mn11Ni4 and Ga137Mn123.

The protein content in crystals and packing coefficients in different space groups.

A precise way of estimating the packing coefficient, i.e. the ratio between the protein and unit-cell volume, or solvent content in protein crystals is given. At present, the solvent content is not given for most proteins in the Protein Data Bank and in many cases where it is given the values are dubious. The mean density of proteins in the crystalline form is around 1.22 g cm(-3), not 1.35 g cm(-3) as usually stated. This is equivalent to 19.5 A(3) per non-H atom. A statistical investigation of the average protein content and packing coefficient in different space groups is presented. The packing coefficients are generally higher in the most frequently occurring space groups than in the uncommon space groups. There is also a remarkable difference in frequency distribution for enantiomorphous pairs of space groups.

Phasing proteins at low resolution.

A method for obtaining phases of low-order reflections is presented. It is based on four observations: (1) the electron density inside proteins is smooth and uniform at low resolution. (2) Since all proteins have almost the same density, the total volume of the protein is known if the molecular weight is known. (3) The overall shape of many proteins is fairly spherical. (4) The total scattering from a sphere of uniform density is in phase with a point scatterer at its centre of gravity, up to a well defined cross-over. After the first cross-over the total protein molecule scatters out of phase with its centre. If the centre of the protein can be found, the phases of typically the ten lowest resolution reflections can be very accurately determined. The method works, provided low-order reflections can be measured accurately and the centre of gravity can be well positioned from these data. The correctly phased low-resolution reflections may be used as a starting set for phase extension. By combining the measured amplitudes with these phases we believe that the size and low-resolution shape of an unknown protein, i.e. the envelope of the molecule, can be obtained.

Two types of mitochondrial crystals in diseased human skeletal muscle fibers.

Mitochondrial crystalline inclusions, frequently found in mitochondrial myopathies, were analyzed by crystallographic techniques and computer-aided image processing. It could be shown that these structures were real crystals. There are two distinct types of crystal, which can be distinguished by shape, size, and pattern. So-called type I crystals are usually present in the intracristal space, whereas the type II crystals are preferentially located in the intermembrane space between outer and inner mitochondrial membranes. The unit cell dimensions were found to be 38 x 34 x 8 nm for the type I crystals and 20 x 17 x 8 nm for the type II crystals. These results strongly suggest that the crystals are composed of macromolecules, presumably proteins. Arguments are presented that indicate that type I crystals occur only in type 1 muscle fibers and type II crystals in type 2 muscle fibers.

Refined crystal structure of liver alcohol dehydrogenase-NADH complex at 1.8 A resolution.

The crystal structure of the ternary complex of horse liver alcohol dehydrogenase (LADH) with the coenzyme NADH and inhibitor dimethyl sulfoxide (DMSO) has been refined by simulated annealing with molecular dynamics and restrained positional refinement using the program X-PLOR. The two subunits of the enzyme were refined independently. The space group was P1 with cell dimensions a = 51.8, b = 44.5, c = 94.6 A, alpha = 104.8, beta = 102.3 and gamma = 70.6 degrees. The resulting crystallographic R factor is 17.3% for 62 440 unique reflections in the resolution range 10.0-1.8 A. A total of 472 ordered solvent molecules were localized in the structure. An analysis of secondary-structure elements, solvent content and NADH binding is presented.

Three-dimensional structure of the crystalline surface layer from Aeromonas hydrophila.

The three-dimensional (3D) structure of the crystalline surface layer of Aeromonas hydrophila has been determined to a resolution of 1.3 nm by crystallographic electron microscopy. The S-layer has tetragonal symmetry, with a unit cell dimension of 12.0 nm and a thickness of 5.6 nm. The 3D reconstruction reveals a distinct domain structure, with one main protein mass at one of the fourfold symmetry axes and a minor part at the other.

Structures of two different surface layers found in six Bacteroides strains.

The structures of crystalline layers from six Bacteroides strains were studied by electron microscopy. Two different hexagonal crystalline surface layers were found, one with a unit cell spacing of 21.5 nm and another with a spacing of 7.7 nm. A three-dimensional structure of the 21.5-nm layer and a two-dimensional projection of the 7.7-nm layer were determined to 3.0- and 3.8-nm resolution, respectively, by computerized image processing of electron micrographs. Both of these two crystalline layers were found in all six strains studied: B. pentosaceus NP333T and WPH61, B. capillus ATCC 33690T and ATCC 33691, and B. buccae ATCC 33574T and ES57. This further supports the identity of B. pentosaceus, B. capillus, and B. buccae as suggested by M. Haapasalo, K. Lounatmaa, H. Ranta, H. Shah, and K. Ranta (Int. J. Syst. Bacteriol. 35:65-72, 1985). The surface layer with 21.5-nm spacing is an intricate network with two classes of pores through the layer.