Extra-large pore zeolite (ITQ-40) with the lowest framework density containing double four- and double three-rings.

The first zeolite structure (ITQ-40) that contains double four (D4) and double three (D3) member ring secondary building units has been synthesized by introducing Ge and NH(4)F and working in concentrated synthesis gels. It is the first time that D3-Rs have been observed in a zeolite structure. As was previously analyzed [Brunner GO, Meier, WM (1989) Nature 337:146-147], such a structure has a very low framework density (10.1 T/1,000 A(3)). Indeed, ITQ-40 has the lowest framework density ever achieved in oxygen-containing zeolites. Furthermore, it contains large pore openings, i.e., 15-member rings parallel to the [001] hexagonal axis and 16-member ring channels perpendicular to this axis. The results presented here push ahead the possibilities of zeolites for uses in electronics, control delivery of drugs and chemicals, as well as for catalysis.

Structure analysis of polymerized phospholipid bilayer by TED and direct methods.

This paper describes the use of elastic energy filtered transmission electron diffraction combined with Direct Methods in order to study the structure of thin Langmuir-Blodgett films of a radiation sensitive diacetylene polymer (DC8.9PC). We obtain a potential map for one projection by direct phasing of zone axis patterns, and discuss experimental problems and possible solutions.

Density histograms in protein electron crystallography-direct phase determination of bacteriorhodopsin at 6A resolution.

Direct methods for crystallographic phase determination have been used to solve the projected structure of native glucose-embedded bacteriorhodopsin (plane group p3, a=62.4A) to 6A, without accepting any information from electron micrographs. After defining the origin and enantiomorph and adding one algebraic phase term to the basis set, expansions into the complete set of 50 unique reflections via the Sayre equation, testing four possible values of the algebraic term, could be screened with figures of merit based on the protein density histogram, where the auto-correlation function of the ideal histogram is an endpoint for the cross-correlation of experimental histogram with this ideal distribution. Initial phase determination, followed by Fourier refinement and some additional phase permutation, yields a solution with an overall mean phase error of 60.8 or 35.4 degrees for the 18 most intense reflections.

Low-resolution direct phase determination in protein electron crystallography - breaking globular constraints.

Although the assumption of an overall globular scattering entity can be useful for determining crystallographic phases for a protein at low resolution, there is a point where this pseudoatomic model must be abandoned for further phase refinement. Using 6 A resolution electron diffraction data from aquaporin (AQP-CHIP) as an example, phases of the 16 most intense reflections from a previous direct solution (Dorset & Jap (1998). Acta Cryst. D54, 615-621) were modified with a Hadamard error-correcting code to produce potential maps very similar to the ones obtained using phases from the Fourier transform of averaged electron micrographs. The choice of the optimal phase set was made via the cross correlation of experimental with anticipated density histograms using the autocorrelation function of the latter histogram as the desired endpoint.

Prospects for kinematical least-squares refinement in polymer electron crystallography.

Least-squares refinement is unusual in the context of electron crystallography because of the sparsity of the measured intensity data set and the problems of systematic errors due to multiple dynamical scattering. With 120 unique hkl electron diffraction intensities measured from polymorphic form III of isotactic poly(1-butene), conditions for improving an existing structural model derived from initial direct structure analysis have been evaluated. The polymer crystallizes in space group P2(1)2(1)2(1) with a = 12.38, b = 8.88, c = 7.56 A and there are 8 unique atoms in the asymmetric unit. Starting with atomic positions resulting from Fourier refinement, four cycles of least-squares refinement, where the positional shifts of atomic positions were constrained, produced better bonding parameters than found before while lowering the conventional crystallographic residual, based on absolute value(F), from an overall value of R = 0.26 to R = 0.185 for the 58 most intense reflections where magnitude of absolute value(Fh(obs)) > or = 4sigma (Fh(obs)) or 0.216 for the complete data set of 120 reflections. The weighted residuals based on magnitude of absolute value(F)2 fell from 0.50 to 0.41 for the complete data set. This refinement was not improved however when attempts were made to fill in very weak intensities by default values. Also, effects of multiple-scattering perturbations were found in the irregularity of the final isotropic thermal parameters.

On the direct determination of three-dimensional crystallographic phases at low resolution: crambin at 6 A.

Using a pseudo-atom approach, the three-dimensional crystallographic phases for the protein crambin (a = 40.76, b = 18.49, c = 22.33 A, beta = 90.61 degrees, space group P2(1)) were determined to 6 A by direct methods. First, the centrosymmetric h0l set was assigned phases by symbolic addition, and the initial solution was then refined by Fourier methods. Phase values of strong reflections were then permuted, and the decision to change the phase value for two of these was made by consulting a cross-correlation of the experimental density histogram to the theoretical or known histogram for the protein. The two-dimensional basis was then extended by the Sayre equation into three dimensions by assigning a phase to a third allowed hkl origin-defining reflection and an algebraic value to another axial reflection. The correct solution was again identified by the histogram correlation, yielding a solution in which the mean phase error for all 98 reflections was 61.5 degrees or 23.1 degrees for the 21 most intense reflections. A parallel study with another protein indicates this method may have general utility.

Filling the missing cone in protein electron crystallography.

The hyper-resolution property of the Sayre equation is explored for extrapolating amplitudes and phases into the missing cone of data left after tilting a representative protein (rubredoxin) to restricted limits in the electron microscope. At 0.6 nm resolution, a reasonable prediction of crystallographic phases can be made to reconstruct the lost information. Best results are obtained if the goniometer tilt value is greater than approximately +/-60 degrees, but some missing information can be restored if the tilt is restricted to +/-45 degrees.

Direct methods in protein electron crystallography--beef liver catalase in its fully hydrated form at room temperature.

The crystal structure of beef liver catalase was determined ab initio in projection to 9 A resolution using electron diffraction data at room temperature from hydrated specimens maintained in an environmental chamber in the electron microscope. A conservative combination of symbolic addition with maximum entropy and likelihood led to a model with a Patterson correlation coefficient C = 0.89 to the observed data. This independent solution could then be compared favorably to a previous 23 A analysis of electron micrographs from frozen hydrated preparations. Prediction of the higher-resolution structure by extension of the lower-resolution image-based phase basis set also gave a good match to the direct-methods solution, particularly for the most intense reflections.

Electron crystallography--accomplishments and challenges.

Electron crystallography is a powerful tool for the quantitative structural characterization of substances that preferentially form thin microcrystals. Because multiple-beam dynamical scattering may cause observed diffraction intensities to deviate significantly from their kinematical values, it is necessary to demonstrate that the conditions favoring ab initio determinations can be established. Review of similar determinations made from electron and X-ray data make clear both the strengths and weaknesses of electron crystallography. With current instrumentation, the major onus now placed on the experimentalist is to optimize specimen preparation so that the resultant diffraction data can be directly interpreted.

Direct phase determination in protein electron crystallography: aquaporin channel-forming integral membrane protein.

The location of helix sites in the projected structure of the aquaporin channel-forming integral membrane protein from bovine red blood cells was determined by multisolution direct methods to a mean accuracy of +/-1.9 A, based on hk0 electron diffraction data extending to 6 A. The structure was assumed to be composed of pseudo-atoms, corresponding to the helix cross sections, and after re-scaling, normalized structure factors were used to order summation operatorn triples according to the A values. Initial phases were found by symbolic addition with algebraic unknowns. Probable solutions could be isolated by an overall Luzzati test for density flatness and restrictions on local density extremes. The best solution was identified by matching Patterson functions, generated from the trial map density sites, to the one calculated from observed intensities.

Symbolic addition in protein electron crystallography--a method for finding projected helices.

The crystal structure of orthorhombic bacteriorhodopsin was determined in projection by direct methods from electron diffraction amplitudes, assuming that, after re-scaling the problem, the Fourier transform of projected alpha-helices could be modeled by atomic scattering factors. A basic set comprising two origin-defining phases, two phase values from sigma 1 triple estimates and an algebraic unknown (resolved early in the phase determination) was extended to a total set of 20 terms, with only two errors. Five helix sites were observed in the first potential map and, after three cycles of Fourier refinement, the rest of the asymmetric unit was found. The overall phase accuracy was 47 degrees or 22 degrees for the 25 most intense reflections.

X-ray Diffraction: A Practical Approach.

X-ray Diffraction: A Practical Approach, C. Suryanarayana and M. Grant Norton, 1998. Plenum Press, New York and London. xiii + 273 pages. (hardback, $49.50, U.S. and Canada; $59.40, elsewhere).It is the aim of this text to teach undergraduates majoring in materials science the use of powder X-ray diffraction for materials characterization. Since it does not treat X-ray diffraction and crystallography in a general way, it would have been better if it were given a more specific title, such as X-Ray Powder Diffraction for Metallurgical Characterization. A Primer and Workbook. As a laboratory course with work pages to be filled out by the student, it might have been spiral-bound to facilitate such use.

The pseudo-atom approach to phase determination in protein electron crystallography--noncentrosymmetric projections.

From an idea proposed by David Harker [Acta Cryst. (1953), 6, 731-736], the assembly of globular subunits in a protein can be treated as pseudo-atoms for normalizaTion of observed electron diffraction intensities. As demonstrated with published data from native or deoxycholate-treated bacteriorhodopsin, a multisolution approach via the Sayre-Hughes equation can then generate phase solutions to 6 A resolution that compare quite favorably with those determined earlier by phase extension. The major problem in such determinations is identification of the best set, especially if no lower-resolution images of the protein are available. (However, 15 to 10 A resolution image-derived phases could be used as a reference set to identify the correct solution). A viable option may be to compare Patterson maps, calculated from trial map peak positions, to the experimental autocorrelation function. Trial phase determinations for the Omp F porin from E. coli outer membrane, on the other hand, are somewhat less successful because the beta-sheet secondary structure is less well modeled by an array of 'globs'.

X-ray crystal structure of cytotoxic oxidized cholesterols: 7-ketocholesterol and 25-hydroxycholesterol.

The cytotoxic cholesterol derivative, 7-ketocholesterol, crystallizes in a monoclinic unit cell, space group P2(1) with a = 11.405 A, b = 6.288 A, c = 35.393 A and beta = 92.75 degrees (Z = 4). Its room temperature crystal structure was solved by direct methods, i.e., the minimal principle via the Shake-and-Bake (SnB) algorithm. In contrast to the continuous chain pattern found for the cholesterol monohydrate structure, hydrogen bonding in the 7-ketocholesterol structure is localized to specific sites via one water molecule that forms linkages between two O3 hydroxyl groups and one keto oxygen. The final weighted R factor for 4562 reflections was 0.144. The 25-hydroxycholesterol also crystallizes in a monoclinic unit cell (P2(1)), with a = 10.840 A, b = 14.533 A, c = 16.093 A and beta = 95.91 degrees (Z = 4). The low temperature structure was solved by DIRDIF. In this instance, molecular packing is anti-parallel in layers stabilized by hydrogen bonding networks via both hydroxyl functions, differing both from cholesterol monohydrate and the 7-ketocholesterol. The final weighted R-factor for 6566 reflections was 0.034. Functional differences of the oxysterols therefore, may be expressed by observed variations in the molecular packing and geometry.

The accurate electron crystallographic refinement of organic structures containing heavy atoms.

Prospects for the accurate structure determination of heavy-atom-containing organic crystals were evaluated with electron diffraction data from perchloro and perbromo derivatives of copper phthalocyanine. While the extensive overlap of experimental Patterson maps (from 1200kV intensities) with respective crystal autocorrelation functions explains the success of previous direct structure analyses, it is clear that multiple-scattering perturbations still evident at high voltage will frustrate the determination of accurate bond distances and angles. If, however, the result obtained after direct structure analysis and Fourier refinement is used to position an idealized molecular model (i.e. with chemically reasonable bonding parameters), the correct structure can then be justified by a rotational search coupled with a multislice dynamical calculation. Even though dynamical scattering is not the only major perturbation to such data sets, the resolution-limited correction is still sufficient to identify the correct molecular orientation in the unit cell. Alternatively, an acceptable unconstrained structure refinement can be carried out via a procedure proposed by Huang, Liu, Gu, Xiong, Fan & Li [Acta Cryst. (1996), A52, 152-157]. A phenomenological adjustment of observed intensities, based initially on the heavy-atom positions found in a high-resolution electron micrograph, will permit all light atoms to be observed near their ideal positions in the ensuing Fourier refinement.

Direct phase determination in protein electron crystallography: the pseudo-atom approximation.

The crystal structure of halorhodopsin is determined directly in its centrosymmetric projection using 6.0-A-resolution electron diffraction intensities, without including any previous phase information from the Fourier transform of electron micrographs. The potential distribution in the projection is assumed a priori to be an assembly of globular densities. By an appropriate dimensional re-scaling, these "globs" are then assumed to be pseudo-atoms for normalization of the observed structure factors. After this treatment, the structure is determined directly by conventional direct methods, followed by Fourier refinement, leading to a mean phase deviation of only 20 degrees (from the values originally found from the image transform) for the 45 most intense reflections.

Prospects for the direct electron crystallographic determination of zeolite structures.

Recently two successful zeolite structures based on experimental electron crystallographic data have been published. Diffraction and image data based on the silicate portion of the zeolite, mordenite, which are perturbed by dynamical (as well as secondary) scattering, have been simulated by a multiple-beam dynamical scattering program. Structure analyses with these data show that the above claims are not unreasonable, given a high enough accelerating voltage for the electron beam. If, for example, 2.9 A resolution micrographs are taken from a 120 A thick crystal in a 200 or 400 kV electron microscope, the crystallographic phases found by image analysis (Fourier filtration) are accurate enough to be extended by the Sayre equation to the (atomic) resolution limit of the electron diffraction pattern (for example from a 105 A thick crystal illuminated by a 1,200 kV electron source). The resultant potential map can be interpreted to find most of the atomic positions and the remaining ones will appear during the progress of a Fourier refinement.

Direct methods in protein electron crystallography: the ab initio structure determination of two membrane protein structures in projection using maximum entropy and likelihood.

Using maximum entropy and likelihood, an ab initio phase determination was carried out in projection at ca 6-10 A resolution for two dissimilar membrane proteins: the Omp F porin from the outer membrane of E. coli (largely beta-sheet) and halorhodopsin (largely alpha-helix). Accurate phase information found for the most likely solutions enabled potential maps to be calculated that contained most of the essential structural details of these macromolecules without the need for any image-derived phases as a starting set for phase extension or the necessity to use envelopes or electron-density histograms. A comparison with earlier calculations using the Sayre-Hughes equation coupled with phase annealing and the Luzzati flatness criterion used as a figure of merit is made.

Electron crystallography.

The idea of solving unknown crystal structures from experimental electron-diffraction intensities and high-resolution electron micrographs has remained a controversial topic in the 60 year history of electron crystallography. In this review it will be shown that the application of modern direct phasing techniques, familiar to X-ray crystallographers, has decisively proven that such ab initio determinations are, in fact, possible. This statement does not, by any means, refute the existence of the several significant scattering perturbations identified by diffraction physicists. Rather, it does affirm that experimental parameters can be controlled to ensure that a 'quasi-kinematical' data set can be collected from many types of specimens. Numerous applications have been made to various types of specimens, ranging from small organics to proteins, and also some inorganic materials. While electron crystallography may not be the optimal means for determining accurate bonding parameters, it is often the method of choice when only microcrystalline specimens are available.

Direct phasing in protein electron crystallography--phase extension and the prospects for ab initio determinations.

Zonal diffraction amplitudes and crystallographic phases, derived from an averaged electron micrograph of two-dimensionally crystalline E. coli Omp F outer membrane porin (plane group p31m, a = 72 A), embedded in glucose, were used as a model data set to test the feasibility of direct phase extension and ab initio direct phase determination. If 17 phase terms derived from e.g. a 10 A (diffraction) resolution image are expanded to 6 A by the Sayre-Hughes equation, the unknown phases are found with reasonable accuracy (mean error 43 degrees for 25 reflections). This, however, is not the most optimal starting point. As a function of initial image resolution, the accuracy of the phase extension to 6 A is approximately a parabolic function. That is, an optimal basis resolution, found at 11 A (i.e. 14 defined reflections), produces a least mean error of 18 degrees for 28 new reflections. In addition, ab initio phase determination is possible via a multisolution technique, using a test for density flatness as a figure of merit. The success of the determination, again is sensitive to the size of the starting basis set generated from the permuted unknown reflections. If an annealing step is used to improve the basis set, the test for flatness will identify which reflections should be changed in phase. However, this figure of merit is not absolutely reliable for finding the exact value of the unknown phases.