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ISSN: 2053-2733

July 2022 issue

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Cover illustration: The random conical tilt technique is used in single-particle cryo-electron microscopy to reconstruct the 3D molecular structure, but involves measuring pairs of images of the same field of view at different tilt angles. In this issue Ti-Yen Lan et al. [Acta Cryst. (2022). A78, 294–301] describe a new method which uses data collected at just one large tilt angle and circumvents the need for particle picking. The image shows the Fourier transforms of the molecular projections from pairs of micrographs collected at different tilt angles assembled in Fourier space with respect to their corresponding orientations (top, standard method) and the structure of myoglobin reconstructed using the new method from noisy micrographs at just one tilt angle (bottom right). The `ground truth' used to simulate the micrographs is shown at the bottom left.

advances

research papers


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A method is described to reconstruct the 3D molecular structure without the need for particle picking in the random conical tilt scheme. The results show promise to reduce the size limit for single-particle reconstruction in cryo-electron microscopy.

short communications


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The longstanding problem of determining the correct point at which to stop the calculations in the X-ray constrained wavefunction (XCW) approach is formally solved on solid mathematical grounds, and a new and more physically meaningful variant of the XCW method is proposed.

foundations

research papers


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Growth forms can be used to study a range of crystallographic problems including obtaining exact formulae for coordination sequences, modeling the structures of nanoclusters and calculating topological densities. While they are fully understood in the periodic case, very little is known about them in the quasiperiodic case. Growth forms of quasiperiodic tilings obtained by the grid method are presented.

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The necessary and sufficient conditions for diffraction enhancement of symmetry in monoarchetypal modular structures are derived.

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Physical properties of objects depend on topological features of the corresponding triply periodic surfaces; thus topological exploration and classification of the surfaces has practical relevance. A general method is developed for generating triply periodic surfaces from triply periodic crystal structures. In 253 zeolite frameworks, 12 surfaces were found to be equivalent to already known triply periodic minimal surfaces (TPMSs), while four surfaces can be treated as new TPMSs.

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Regular polyhedra and related structures such as complexes and nets play a prominent role in the study of materials such as crystals, nanotubes and viruses. This work discusses an approach to the theory of realizations of abstract regular polyhedra with an emphasis on the construction of a realization and its decomposition as a blend of subrealizations. To demonstrate the approach, it is applied to the polyhedra whose automorphism groups are abstractly isomorphic to the non-crystallographic Coxeter group H3.

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X-ray third-order nonlinear asymmetrical Bragg diffraction is investigated.

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A color code for chair tilings in arbitrary dimensions is presented. The code can be applied also to other lattice substitution tilings.

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The first enumeration and tabulation of all non-equivalent (3+d)-dimensional magnetic superspace groups for d = 1, 2 and 3 independent modulations is presented. An algorithm for uniquely identifying an arbitrary magnetic superspace group with an entry in this tabulation makes it straightforward to establish whether or not two incommensurate magnetic structures with apparently different symmetry operations actually have the same magnetic superspace group, but presented in different settings.

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Using the method of cone types, the coordination sequences (also known as growth functions) of the wallpaper groups (the 2D crystallographic groups) are computed.

obituaries


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