Douglas L. Dorset

Crystallography of waxes-an electron diffraction study of refined and natural products

The crystal structure of four waxes has been investigated by electron crystallography. Two of these waxes, including a refined petroleum product (Gulfwax) and a material from lignite (montan wax), form well ordered crystals and their structure could be solved quantitatively from the observed diffraction patterns. As also found previously for simpler binary n-paraffin solid solutions, the average structure resembles that of a pure paraffin (e.g. n-) but with a Gaussian distribution of atomic occupancies near the chain ends to account for the statistical distribution of chain lengths within a lamella. Two other waxes from living organisms, South African bee honeycomb and the leaves of the Brazilian carnauba palm, are much less ordered, even though they share the same methylene subcell packing of the most crystalline parts of the previous materials. It appears that these waxes cannot fully separate into distinct lamellae, perhaps due to the presence of very long `tie molecules, and are therefore `frustrated crystal structures.

Development of lamellar structures in natural waxes - an electron diffraction investigation

When they are recrystallized from the melt, natural plant or insect waxes tend to form solid phases with a nematic-like structure (i.e. a parallel array of polymethylene chains with little or no aggregation of the molecules into distinct layers). An electron diffraction study of carnauba wax and two types of beeswax has shown that the degree of molecular organization into lamellar structures can be enhanced by annealing in the presence of benzoic acid, which also acts as an epitaxial substrate. Nevertheless, the resultant layer structure in the annealed solid is not the same as that found for paraffin wax fractions refined from petroleum. Probably because of a small but significant fraction of a very long chain ingredient, the lamellar separation is incomplete, incorporating a number of `bridging molecules that span the nascent lamellar interface.The same phenomenon has been described recently for a low molecular weight polyethylene.

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.

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.

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°, but some missing information can be restored if the tilt is restricted to ±45°. Microsc. Res. Tech. 46:98–103, 1999.

Crystallization and Data Collection

In electron crystallography, preparation of suitably thin, oriented crystalline samples is vital to the success of an ab initio structure analysis. In certain cases, special measures must be taken to protect the crystals from the ultrahigh vacuum of the electron microscope column, else they will not remain ordered. It might also be desirable to carry out dynamic experiments (e.g., heating/cooling) on these samples while preserving their chemical integrity. These requirements dictate the type of preparative procedures that must be followed and, sometimes, call for special attachments to the electron microscope.

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 Å resolution micrographs are taken from a 120 Å 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 Å 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. Microsc. Res. Tech. 36:212–223, 1997.

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.

Structural framework of a medium Fischer-Tropsch wax fraction determined by electron crystallography

The structural framework of a medium hardness Fischer-Tropsch wax distillate is established quantitatively by electron crystallography and compared to model paraffin assemblies with a similar Gaussian distribution of chain lengths. The lamellar packing closely resembles the crystal structure of refined petroleum waxes with a similar distribution of defects near the lamellar interface. Nevertheless, clear differences associated with the absorption of smaller chains within the lamellar interface, detected by NMR, are not resolved by these diffraction measurements, perhaps due to artefacts induced by the high vacuum of the experiment and/or specimen preparation.

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.