Cryo-Electron Microscopy of the Giant Viruses

High resolution study of the giant viruses presents one of the latest challenges in cryo-electron microscopy of viruses. Too small for light microscopy, but too large for easy study at high resolution by electron microscopy, they range in size from ~0.2-2 μm, from high symmetry icosahedral viruses such as Paramecium burseria Chlorella virus 1 to asymmetric forms like Tupanvirus or Pithovirus. To attain high resolution, two strategies exist to study these large viruses by cryo-EM: firstly, increasing the acceleration voltage of the electron microscope to improve sample penetration and overcome the limitations imposed by electro-optical physics at lower voltages, and secondly the method of “block-based reconstruction” pioneered by Michael G. Rossmann and his collaborators, which resolves the latter limitation through an elegant leveraging of high symmetry, but cannot overcome sample penetration limitations. In addition, more recent advances in both computational capacity and image processing also yield assistance in studying the giant viruses. Especially, the inclusion of Ewald sphere correction can provide large improvements in attainable resolutions for 300 kV electron microscopes. Despite this, the study of giant viruses remains a significant challenge.

Investigation of measurement data of low-coherence interferometry at tilted surfaces in the 3D spatial frequency domain

The 3D transfer characteristics of interference microscopes and their effect on the interference signals occurring at surface slopes are studied. The interference image stacks acquired during a depth scan are 3D Fourier transformed. This allows a comprehensive frequency domain analysis of the interferograms. The double foil model introduced in a previous publication enables the interpretation of the signal spectra and the underlying transfer behavior of the interferometer using the concept of the Ewald sphere, which is limited by the numerical aperture (NA) of the imaging system. Analysis in the 3D spatial frequency domain directly discloses that the lateral dimensions of the transfer function depend on the axial spatial frequency. In this contribution we investigate measuring objects produced by Nanoimprint-Lithography. The corresponding signal spectra bear information that can be utilized to optimize the subsequent signal processing algorithms. These include envelope and phase evaluation procedures of the interference signals. A narrow bandpass filter is used to actively select certain frequency components in order to improve the robustness of the estimation of the envelope position. Although the shape and width of the envelope are affected, this procedure increases the reliability of the evaluation process and improves the accuracy of the measured topography especially at steeper surface slopes.

Quasi-phase-matching-division multiplexing holography in a three-dimensional nonlinear photonic crystal

Nonlinear holography has recently emerged as a novel tool to reconstruct the encoded information at a new wavelength, which has important applications in optical display and optical encryption. However, this scheme still struggles with low conversion efficiency and ineffective multiplexing. In this work, we demonstrate a quasi-phase-matching (QPM) -division multiplexing holography in a three-dimensional (3D) nonlinear photonic crystal (NPC). 3D NPC works as a nonlinear hologram, in which multiple images are distributed into different Ewald spheres in reciprocal space. The reciprocal vectors locating in a given Ewald sphere are capable of fulfilling the complete QPM conditions for the high-efficiency reconstruction of the target image at the second-harmonic (SH) wave. One can easily switch the reconstructed SH images by changing the QPM condition. The multiplexing capacity is scalable with the period number of 3D NPC. Our work provides a promising strategy to achieve highly efficient nonlinear multiplexing holography for high-security and high-density storage of optical information.

Crystallography and Diffraction

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

The modulus of the Fourier transform on a sphere determines 3-dimensional convex polytopes

Let 𝒫 and P ′ \mathcal{P}^{\prime} be 3-dimensional convex polytopes in R 3 \mathbb{R}^{3} and S ⊆ R 3 S\subseteq\mathbb{R}^{3} be a non-empty intersection of an open set with a sphere. As a consequence of a somewhat more general result it is proved that 𝒫 and P ′ \mathcal{P}^{\prime} coincide up to translation and/or reflection in a point if | ∫ P e - i ⁢ s ⋅ x ⁢ dx | = | ∫ P ′ e - i ⁢ s ⋅ x ⁢ dx | \bigl{\lvert}\int_{\mathcal{P}}e^{-i\mathbf{s}\cdot\mathbf{x}}\,\mathbf{dx}\bigr{\rvert}=\bigl{\lvert}\int_{\mathcal{P}^{\prime}}e^{-i\mathbf{s}\cdot\mathbf{x}}\,\mathbf{dx}\bigr{\rvert} for all s ∈ S \mathbf{s}\in S . This can be applied to the field of crystallography regarding the question whether a nanoparticle modelled as a convex polytope is uniquely determined by the intensities of its X-ray diffraction pattern on the Ewald sphere.

Beyond integration: modeling every pixel to obtain better structure factors from stills

Most crystallographic data processing methods use pixel integration. In serial femtosecond crystallography (SFX), the intricate interaction between the reciprocal lattice point and the Ewald sphere is integrated out by averaging symmetrically equivalent observations recorded across a large number (104−106) of exposures. Although sufficient for generating biological insights, this approach converges slowly, and using it to accurately measure anomalous differences has proved difficult. This report presents a novel approach for increasing the accuracy of structure factors obtained from SFX data. A physical model describing all observed pixels is defined to a degree of complexity such that it can decouple the various contributions to the pixel intensities. Model dependencies include lattice orientation, unit-cell dimensions, mosaic structure, incident photon spectra and structure factor amplitudes. Maximum likelihood estimation is used to optimize all model parameters. The application of prior knowledge that structure factor amplitudes are positive quantities is included in the form of a reparameterization. The method is tested using a synthesized SFX dataset of ytterbium(III) lysozyme, where each X-ray laser pulse energy is centered at 9034 eV. This energy is 100 eV above the Yb3+ L-III absorption edge, so the anomalous difference signal is stable at 10 electrons despite the inherent energy jitter of each femtosecond X-ray laser pulse. This work demonstrates that this approach allows the determination of anomalous structure factors with very high accuracy while requiring an order-of-magnitude fewer shots than conventional integration-based methods would require to achieve similar results.

Defocus-dependent Thon-ring fading

ABSTRACTThe brightness of modern Schottky field-emission guns can produce electron beams that have very high spatial coherence, especially for the weak-illumination conditions that are used for single-particle electron cryo-microscopy in structural biology. Even so, many users have observed defocus-dependent Thon-ring fading that has led them to restrict their data collection strategy to imaging with relatively small defocus values. In this paper, we reproduce the observation of defocus-dependent Thon-ring fading and produce a quantitative analysis and clear explanation of its causes. We demonstrate that a major cause is the delocalization of high-resolution Fourier components outside the field of view of the camera. We also show that it is important to make a correction for linear magnification anisotropy, even if it is quite small, before circular averaging of the Thon rings, as is also true before merging data from particles in many orientations. Under the conditions used in this paper, which are typical of those used in single-particle electron cryomicroscopy, fading of the Thon rings due to source coherence is negligible. The principal conclusion is that much higher values of defocus can be used than is currently thought to be possible. This increased understanding should give electron microscopists the confidence to use higher amounts of defocus to allow, for example, better visibility of their particles and Ewald sphere correction.

Practical Aspects of Neutron Scattering

In this chapter, aspects of the planning and optimization of a neutron scattering experiment are covered, including attenuation, multiple scattering, data normalization, counting statistics, resolution, corrections for polarization analysis, and spurions. Practical aspects of diffraction experiments are described, including instrumentation, Rietveld refinement, anisotropic displacement parameters, the Ewald sphere construction, Lorentz factors, extinction and multiple scattering. Practical aspects of spectroscopy are also described, including triple-axis, time-of-flight and backscattering spectrometers, direct and indirect geometry, and some specific points arising in time-of flight inelastic scattering.

New tools for automated high-resolution cryo-EM structure determination in RELION-3

Here, we describe the third major release of RELION. CPU-based vector acceleration has been added in addition to GPU support, which provides flexibility in use of resources and avoids memory limitations. Reference-free autopicking with Laplacian-of-Gaussian filtering and execution of jobs from python allows non-interactive processing during acquisition, including 2D-classification, de novo model generation and 3D-classification. Per-particle refinement of CTF parameters and correction of estimated beam tilt provides higher resolution reconstructions when particles are at different heights in the ice, and/or coma-free alignment has not been optimal. Ewald sphere curvature correction improves resolution for large particles. We illustrate these developments with publicly available data sets: together with a Bayesian approach to beam-induced motion correction it leads to resolution improvements of 0.2–0.7 Å compared to previous RELION versions.