Biomedical subjects

D L Dorset

Publications and source records attributed to D L Dorset.

At least 19 recordsLinked to original sources

PubMed1998

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.

Crystallography↗

PubMed1998

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.

Animals↗

PubMed1998

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.

Bacteriorhodopsins↗

PubMed1997

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'.

Bacterial Outer Membrane Proteins↗

PubMed1997

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.

Crystallization↗

PubMed1997

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.

Bacteriorhodopsins↗

PubMed1997

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.

Aluminum Silicates↗

PubMed1997

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.

Crystallization↗

PubMed1996

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.

Bacteriorhodopsins↗

PubMed1996

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.

Crystallography↗

PubMed1996

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.

Crystallography↗

PubMed1995

The crystal structure of waxes.

Quantitative electron crystallographic studies have been carried out on epitaxially oriented multi-component waxes. Intensities from two paraffin-based samples, an artificial six-component medium wax (equimolar distribution of chain lengths) and a petroleum-based wax (Gaussian distribution of chain lengths) have been used to determine their crystal structures. As found earlier for binary paraffin solid solutions, differences in molecular volume are compensated by longitudinal molecular shifts within individual lamellae. Nevertheless, each lamellar surface must remain flat enough, and with enough crystallographic order intact, to nucleate the next lamella, thus accounting for the observed long-range correlation in these crystals. Recrystallized beeswax also has a layer packing somewhat similar to the paraffin waxes. However, in this case, the lamellar order is 'frustrated' so that a certain amount of 'nematically' ordered material must be present, spanning the nascent lamellar interfaces.

Animals↗

PubMed1995

Direct structure analysis in protein electron crystallography: crystallographic phases for halorhodopsin to 6-A resolution.

The crystal structure of halorhodopsin was determined in (centrosymmetric) projection to 6-A resolution by direct methods that use only the amplitudes of the electron diffraction pattern. A multisolution technique was used to generate initial 15-A-resolution basis sets, and after selection of the best phase set (by the closest match of magnitude of Eobs and magnitude of Ecalc), annealing of individual reflections was used to improve its accuracy. The Sayre equation was then used to expand the phase terms to 10 A, followed again by phase annealing. A final expansion with the Sayre equation enlarged this corrected phase set to 6 A. When the condition of density flatness was used to locate the best phase solution after each extension, a final structure could be observed that was quite similar to the one found earlier by analysis of electron micrographs.

Bacteriorhodopsins↗

PubMed1995

The Sayre equation in electron crystallography.

The Sayre equation was evaluated as a technique for phase refinement in electron crystallography. Atomic-resolution electron diffraction data from copper perchlorophthalocyanine were assigned phase values from the Fourier transforms of various experimental electron micrographs, including one at 2.3 A, containing errors due to lens astigmatism. In each case, an atomic-resolution structure could be found after Fourier refinement. In addition, it was possible to begin with a basis set derived from symbolic addition for phase extension. Such a source of phases was also found to be useful for extending zonal electron diffraction sets from six polymer crystals, even though there was considerable overlap of atomic positions in the projection down the chain axes. Other tests of the Sayre equation were made with zonal protein data sets (bacteriorhodopsin, halorhodopsin) to evaluate what difficulties are to be expected when direct phasing techniques are to be used in macromolecular electron crystallography. Comparison to known values indicated that the low-resolution range (e.g. to 6 A) was reasonably stable for phase extension from a 10-15 A resolution image. Only when a minimum in average intensity was approached (near 5 A) did the direct extension encounter serious difficulties. If this minimum was treated as a "phase node" to generate two possible solutions, a model more similar to the true phase set was found. In general, this rather simple convolutional technique for phase extension seems to be particularly suitable for a variety of electron crystallographic applications.

Crystallography↗

PubMed1995

Direct structure determination by electron crystallography: protein data sets.

Applications of the Sayre equation to the electron crystallographic analysis of protein structures are demonstrated. Starting with a lower-resolution basis phase set obtained from the Fourier-transform of an electron micrograph, it is possible, for example, to extend directly to the higher resolution of the electron diffraction pattern. Examples of such analyses include bacteriorhodopsin, halorhodopsin and the Omp F porin from the outer membrane of Escherichia coli. If a multisolution approach is taken, it may also be possible to carry out ab initio phase determinations, as demonstrated with low-resolution diffraction amplitudes from a negatively-stained membrane protein crystal.

Bacterial Outer Membrane Proteins↗

PubMed1994

Direct determination of layer packing for a phospholipid solid solution at 0.32-nm resolution.

Electron diffraction intensity data were collected from a 2:3 binary solid solution of two homologous phosphatidylethanolamines (1,2-dimyristoyl-sn-glycerophosphoethanolamine and 1,2-dipalmitoyl-sn-glycerophosphoethanolamine) epitaxially oriented by cocrystallization with naphthalene. The layer packing was determined directly by predicting the value of 12 of the 17 phases from sigma 1- and sigma 2-triplet invariants in space group P1. A reverse Fourier transform of the resulting potential maps provides estimates for three other phases and the two remaining ones were found by generating maps for the 2(2) = 4 possible phase combinations and then testing the smoothness of the potential profile of the hydrocarbon chain packing. The same phase solution can be found by translating a molecular model (based on the known x-ray crystal structure of a shorter homologue) past the unit cell origin. The solid solution is found to retain a stable polar group packing while the statistical occupancy of two terminal-chain carbons is expressed by a reduced potential profile at the nonpolar interface at the bilayer center.

Crystallography, X-Ray↗

PubMed1994

Electron crystallography of organic and biological molecules--techniques and comparison to X-ray crystallographic results.

In this review, it is shown how ab initio analyses of molecular crystal structures can be carried out with electron diffraction intensities and high-resolution, low-dose, electron micrographs, dispelling the long-held myth that such determinations are not possible. The results for small organics, polymethylene compounds, various polymers, and even intregral membrane proteins, are in good agreement with independent X-ray crystal structure determinations, which, however, were not needed to solve the crystallographic phase problem from the electron scattering data. The concept of electron crystallography benefits from the utility of electron micrographs for providing phase information, in addition to the standard 'direct' methods used nowadays by all crystallographers.

Crystallography↗

PubMed1994

Structural determination and packing analysis of a cholesteryl caprate/cholesteryl laurate solid solution.

This paper describes the X-ray crystal structure analysis of a cholesteryl ester solid solution, cholesteryl decanoate/cholesteryl laurate, grown from a bulk concentration with molar ratio 0.56/0.43. The unit cell is monoclinic with a = 12.969, b = 9.048, c = 31.137 A, and beta = 91.12 degrees and the space group P2(1) with Z = 4 (two molecules per asymmetric unit). The cell constants closely represent an average value of crystal parameters for the two pure components (hence, nearly corresponding to Vegard's law). Although the overall monolayer 1 lamellar packing is superficially similar to the earlier-studied cholesteryl undecanoate/cholesteryl laurate solid solution, a more partitioned distribution of acyl chains, i.e., a microfractionation corresponding to the observed nonideal phase behavior, is suggested. The behavior is similar to that found for n-paraffin binaries cooled below a binodal phase boundary. Although it cannot be detected conclusively in this determination (due to high thermal motion of terminal acyl chain atoms), the non-stoichiometric combination of components also requires some partial occupancy of atomic sites on the chain termini. This structural arrangement is contrasted with the alternative expression found earlier for the more ideal undecanoate/laurate solid solution, i.e., random co-packing leading to fractional atomic occupancy in an average laurate structure. The final weighted R factor for 4578 reflections is 0.138.

Cholesterol Esters↗