Direct phase determination in electron crystallography: The crystal structure of an n-paraffin

Atomic-Scale Corrugations in Crystalline Polypeptoid Nanosheets Revealed by Three-Dimensional Cryogenic Electron Microscopy

Amphiphilic molecules that can crystallize often form molecularly thin nanosheets in aqueous solutions. The possibility of atomic-scale corrugations in these structures has not yet been recognized. We have studied the self-assembly of amphiphilic polypeptoids, a family of bio-inspired polymers that can self-assemble into various crystalline nanostructures. Atomic-scale structure of the crystals in these systems has been inferred using both X-ray diffraction and electron microscopy. Here we use cryogenic electron microscopy to determine the in-plane and out-of-plane structures of a crystalline nanosheet. Data were collected as a function of tilt angle and analyzed using a hybrid single-particle crystallographic approach. The analysis reveals that adjacent rows of peptoid chains, which are separated by 4.5 Å in the plane of the nanosheet, are offset by 6 Å in the direction perpendicular to the plane of the nanosheet. These atomic-scale corrugations lead to a doubling of the unit cell dimension from 4.5 to 9 Å. Our work provides an alternative interpretation for the observed Å X-ray diffraction peak often reported in polypeptoid crystals.

Effect of processing and end groups on the crystal structure of polypeptoids studied by cryogenic electron microscopy at atomic length scales

Cryogenic electron microscopy at atomic length scales was used to study the structure of self-assembled crystalline nanosheets obtained from a series of polypeptoids with the same chain architecture but with different end groups. While long-range order is enhanced by slowing down the self-assembly process, the dominant crystalline motif was found to be a sensitive function of both processing details and end group chemistry. In some cases, adjacent rows of polypeptoid molecules adopt anti-parallel V-shaped side chain conformations. In other cases, adjacent rows of polypeptoid molecules adopt parallel V-shaped side chain conformations. Interestingly, the unit cell is rectangular in both cases with dimensions a = 4.5 Å and c = 50 Å. In all cases, long-range order, quantified by the average number of concatenated unit cells of the same type, is more prevalent along the a direction.

Electron crystallography of the polymethylene chain. 4. Defect distribution in lamellar interfaces of paraffin solid solutions

As is also found for paraffin lamellar crystals heated near the rotator or melt transition, the major change in electron diffraction patterns imposed by lamellar disorder in binary or multicomponent solid solutions is the attenuation and intensity modification of low-angle (00l) reflections. Using a Gaussian model for atomic occupancies near the interface, a systematic basis is found for the interfacial disorder thickness, describing the phenomenological ‘void’ distribution at the lamellar interface. (Vibrational spectroscopy has shown that this is actually a distribution of non-planar chain conformations.) Single crystal electron diffraction data from various co-soluble paraffin chain assemblies, used previously to determine their crystal structures (but also including a new determination for n-C36H74/ n-C38H78/ n-C40H82 1: 1: 1), are re-analyzed so that further distinctions can be made among simple binary and ternary solid solutions, multicomponent waxes, and low molecular weight polyethylene. Expressions of the latter polyethylene structure, involving ‘bridging molecules’ can be found in certain natural insect and plant waxes.

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.

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.

Electron crystallography at atomic resolution: ab initio structure analysis of copper perchlorophthalocyanine

High-voltage (1200 kV) electron diffraction intensities from approximately 100 A thick crystals of copper perchlorophthalocyanine are used to determine the molecular packing at atomic resolution, thus greatly exceeding the structure detail observed by electron microscopy. Initial crystallographic phases were determined by direct methods often used in X-ray crystallography, i.e., locating the positions of heavy (Cl and Cu) atoms in the structure. All other atom positions were found in subsequent Fourier refinement (final R = 0.28). Calculated bond distances and angles are similar to those found in the earlier X-ray crystal structure of the unchlorinated parent compound.