X-ray crystallography

X-ray crystallography
Name	X-ray crystallography
Caption	A fundamental principle of the technique
Classification	Diffraction, Crystallography
Inventors	Max von Laue, William Henry Bragg, William Lawrence Bragg
Related	Neutron diffraction, Electron diffraction

X-ray crystallography is a powerful analytical technique used to determine the atomic and molecular structure of a crystal. By measuring the angles and intensities of X-ray beams diffracted by the crystalline lattice, a three-dimensional picture of the density of electrons within the crystal can be produced. This allows for the precise determination of the positions of atoms, their chemical bonds, and overall molecular conformation. The method has been foundational in numerous scientific breakthroughs across chemistry, materials science, and structural biology.

Principles and theory

The technique is grounded in the wave nature of X-rays and the periodic arrangement of atoms in a crystal. When an incident X-ray beam strikes a crystal, the electrons of the atoms scatter the radiation. The scattered waves constructively interfere in specific directions, governed by Bragg's law, which relates the diffraction angle to the spacing between crystal lattice planes. This law, formulated by William Lawrence Bragg, is the cornerstone for interpreting diffraction patterns. The resulting diffraction pattern is a Fourier transform of the crystal's electron density, and the mathematical process of reversing this transform to obtain an atomic model is known as Fourier synthesis.

Experimental setup

A standard apparatus consists of an X-ray source, such as a sealed tube or a synchrotron, which generates a monochromatic beam. The crystal, typically mounted on a goniometer, is precisely aligned and rotated to expose all crystallographic planes to the beam. The diffracted rays are recorded by a detector, historically photographic film but now almost exclusively electronic devices like charge-coupled device (CCD) or pixel array detectors. For protein crystallography, the sample is often cryo-cooled with liquid nitrogen to reduce radiation damage. Key components also include collimators to define the beam and monochromators to select specific wavelengths.

Data collection and analysis

The process begins with obtaining a high-quality single crystal and collecting a full set of diffraction images at various orientations. The intensities of thousands of reflection spots are measured and corrected for factors like absorption and Lorentz-polarization. The initial phase of each diffracted wave, which is lost in measurement, must be determined through methods like molecular replacement, isomorphous replacement, or anomalous dispersion. Using specialized software such as PHENIX or CCP4, the electron density map is calculated and an atomic model is built into it. The model is then refined against the data using least squares or maximum likelihood algorithms to minimize the discrepancy, reported as the R-factor.

Applications

This technique has been instrumental in determining the structures of countless materials, from simple salts to complex macromolecules. In structural biology, it revealed the double-helix structure of DNA by Rosalind Franklin, James Watson, and Francis Crick, and the intricate folds of proteins like hemoglobin and lysozyme. It enabled the design of pharmaceuticals, such as HIV protease inhibitors, through structure-based drug design. In inorganic chemistry, it elucidates the architecture of zeolites and metal-organic frameworks. The method was also crucial for the discovery of quasicrystals by Dan Shechtman, which challenged classical crystallography.

Limitations and challenges

A primary requirement is the growth of a well-ordered, single crystal of adequate size, which can be prohibitively difficult for many biological macromolecules or complex materials. The technique provides a static, time-averaged snapshot and generally cannot capture dynamic processes or transient states without specialized methods like time-resolved crystallography. Radiation damage, particularly from intense synchrotron beams, can degrade samples. For very large structures like ribosomes or virus capsids, phasing remains a significant hurdle. Furthermore, the presence of disorder within the crystal lattice can obscure or complicate the interpretation of electron density maps.

Historical development

The field originated with the discovery of X-ray diffraction by crystals in 1912 by Max von Laue and his assistants Walter Friedrich and Paul Knipping, for which von Laue received the Nobel Prize in Physics in 1914. William Henry Bragg and his son William Lawrence Bragg quickly developed the foundational law and equipment, earning the 1915 Nobel Prize in Physics. Pioneering work by Kathleen Lonsdale on benzene and Dorothy Hodgkin on the structure of penicillin and vitamin B12 demonstrated its power in organic chemistry. The development of direct methods by Herbert Hauptman and Jerome Karle, and the advent of synchrotron radiation sources, dramatically expanded the scope and efficiency of the technique.

Category:Crystallography Category:Scientific techniques