Opening crystallography

Structural Chemistry - This essay surveys results of the past 4 years, starting with a week-long workshop on “Soft Packings, Nested Clusters, and Condensed Matter” held in...     

Fast quantum crystallography

Typical contemporary X-ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R-factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.     

History of X-ray crystallography

A brief account is given of the history of X-ray crystallography from its beginning in 1912 to the present time. Particular emphasis is placed on the phase problem, the major obstacle in the path leading from the observed X-ray diffraction pattern to the desired crystal structure. The essential role which mathematics plays in resolving this problem is also stressed.     

Milestones in electron crystallography

Electron crystallography determines the structure of membrane embedded proteins in the two-dimensionally crystallized state by cryo-transmission electron microscopy imaging and computer structure reconstruction. Milestones on the path to the structure are high-level expression, purification of functional protein, reconstitution into two-dimensional lipid membrane crystals, high-resolution imaging, and structure determination by computer image processing. Here we review the current state of these methods. We also created an Internet information exchange platform for electron crystallography, where guidelines for imaging and data processing method are maintained. The server (http://2dx.org) provides the electron crystallography community with a central information exchange platform, which is structured in blog and Wiki form, allowing visitors to add comments or discussions. It currently offers a detailed step-by-step introduction to image processing with the MRC software program. The server is also a repository for the 2dx software package, a user-friendly image processing system for 2D membrane protein crystals.     

X-ray crystallography and chirality: understanding the limitations

Advances in hardware and software have made X-ray crystallography even more attractive as the first-option method for structure analysis. For most organic materials containing up to 100 non-hydrogen atoms, getting from the initial visual examination of the sample to producing publication-ready tables and pictures should usually be achievable in a single morning. Improvements in hardware have also increased reliability of the determination of absolute configuration. A recently published new algorithm may extend the range of applicability of the method.     

Macromolecular crystallography research at Trombay

Neutron diffraction studies of hydrogen positions in small molecules of biological interest at Trombay have provided valuable information that has been used in protein and enzyme structure model-building and in developing hydrogen bond potential functions. The new R-5 reactor is expected to provide higher neutron fluxes and also make possible smallangle neutron scattering studies of large biomolecules and bio-aggregates. In the last few years infrastructure facilities have also been established for macromolecular x-ray crystallography research. Meanwhile, the refinement of carbonic hydrases’ and lysozyme structures have been carried out and interesting results obtained on protein dynamics and structure-function relationships. Some interesting presynaptic toxin phospholipases have also been taken up for study.     

Quantum crystallography: A perspective

Extraction of the complete quantum mechanics from X‐ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X‐ray diffraction data into an electron density that reflects the antisymmetry of an N‐electron wave function. A formalism for this was developed early on for the determination of a constrained idempotent one‐body density matrix. The formalism ensures pure‐state N‐representability in the single determinant sense. Applications to crystals show that quantum mechanical density matrices of large molecules can be extracted from X‐ray scattering data by implementing a fragmentation method termed the kernel energy method (KEM). It is shown how KEM can be used within the context of quantum crystallography to derive quantum mechanical properties of biological molecules (with low data‐to‐parameters ratio). © 2017 Wiley Periodicals, Inc.     

Interstitial fractionalization and spherical crystallography

Finding the ground states of identical particles packed on spheres has relevance for stabilizing emulsions and has a venerable history in the literature of theoretical physics and mathematics. Theory and experiment have confirmed that defects such as disclinations and dislocations are an intrinsic part of the ground state. Here we discuss the remarkable behavior of vacancies and interstitials in spherical crystals. The strain fields of isolated disclinations forced in by the spherical topology literally rip interstitials and vacancies apart, typically into dislocation fragments that combine with the disclinations to create small grain-boundary scars. The fractionalization is often into three charge-neutral dislocations, although dislocation pairs can be created as well. We use a powerful, freely-available computer program to explore interstitial fractionalization in some detail, for a variety of power-law pair potentials. We investigate the dependence on initial conditions and the final state energies, and compare the position dependence of interstitial energies with the predictions of continuum elastic theory on the sphere. The theory predicts that, before fragmentation, interstitials are repelled and vacancies are attracted from 5-fold disclinations. We also use vacancies and interstitials to study low-energy states in the vicinity of "magic numbers" that accommodate regular icosadeltahedral tessellations.     

On the origins of isomorphous replacement in protein crystallography

Structural Chemistry -     

Electron crystallography of epitaxially grown paraffin

Three-dimensional electron diffraction data from the epitaxially crystallized paraffin n-C₃₆H₇₄ are investigated in a structure analysis and are found to give a reasonable image of the structure, in agreement with the earlier x-ray determination. An inconsistency in the refined isotropic temperature factors from different zonal projections, however, indicates the necessity for a more accurate physical model for epitaxially grown crystals which will account for a large spread of diffraction peaks along reciprocal lattice lines parallel to the projection axis.     

An NMR crystallography investigation of furosemide

This paper presents an NMR crystallography study of three polymorphs of furosemide. Experimental magic-angle spinning (MAS) solid-state NMR spectra are reported for form I of furosemide, and these are assigned using density-functional theory (DFT)-based gauge-including projector augmented wave (GIPAW) calculations. Focusing on the three known polymorphs, we examine the changes to the NMR parameters due to crystal packing effects. We use a recently developed formalism to visualise which regions are responsible for the chemical shielding of particular sites and hence understand the variation in NMR parameters between the three polymorphs.     

High-throughput protein crystallography and drug discovery

Single crystal X-ray diffraction is the technique of choice for studying the interactions of small organic molecules with proteins by determining their three-dimensional structures; however the requirement for highly purified protein and lack of process automation have traditionally limited its use in this field. Despite these shortcomings, the use of crystal structures of therapeutically relevant drug targets in pharmaceutical research has increased significantly over the last decade. The application of structure-based drug design has resulted in several marketed drugs and is now an established discipline in most pharmaceutical companies. Furthermore, the recently published full genome sequences of Homo sapiens and a number of micro-organisms have provided a plethora of new potential drug targets that could be utilised in structure-based drug design programs. In order to take maximum advantage of this explosion of information, techniques have been developed to automate and speed up the various procedures required to obtain protein crystals of suitable quality, to collect and process the raw X-ray diffraction data into usable structural information, and to use three-dimensional protein structure as a basis for drug discovery and lead optimisation.This tutorial review covers the various technologies involved in the process pipeline for high-throughput protein crystallography as it is currently being applied to drug discovery. It is aimed at synthetic and computational chemists, as well as structural biologists, in both academia and industry, who are interested in structure-based drug design.     

A zigzag path through quantum crystallography

A brief discussion is given here of recollections related to development of quantum crystallography from a personal point of view of the author.     

Solid-state NMR crystallography through paramagnetic restraints

Pseudocontact shifts (PCSs) measured by solid-state NMR spectroscopy (SS-NMR) on microcrystalline powders of a paramagnetic metalloprotein permit NMR crystallography. Along with other restraints for SS-NMR experiments, the protein molecular structure as well as the correct crystal packing are obtained.     

The use of crystallography for the studies of semiconductor materials

The effect of sublattices on the electronic structure of Zn₂SiO₄ crystals is ab initio studied from the first principles calculations at the density functional theory level. Based on the analysis of band spectra and sublattices the different role of Zn and Si cations in the formation of the valence band structure is determined, which is due to the crystal structure and atomic interactions in SiO₄ and ZnO₄ cationic tetrahedra.