X-ray crystallography

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X-ray crystallography or single-crystal X-ray diffraction is an analytical technique which uses the diffraction pattern produced by bombarding a single crystal with X-rays to solve the crystal structure. The diffraction pattern is recorded and then analyzed or "solved" to reveal the nature of the crystal. This technique is widely used in chemistry and biochemistry to determine the structures of an immense variety of molecules, including inorganic compounds, DNA, and proteins. When single crystals are not available, related techniques such as powder diffraction or thin film x-ray diffraction coupled with lattice refinement alogrithms such as Rietveld refinement may be used to extract similar, though less complete, information about the nature of the crystal.

The spacing in the crystal lattice can be determined using Bragg's law. The electrons that surround the atoms, rather than the atomic nuclei themselves, are the entities that physically interact with the incoming X-ray photons.

[edit] Inorganic & simple organic structures

A diffractometer

In inorganic chemistry, x-ray crystallography is used to determine lattice structures as well as chemical formulae, bond lengths and angles. The primary methods used in inorganic structures are powder diffraction and single-crystal diffraction.

[edit] Single Crystal Diffraction

Many complicated inorganic and organometallic systems have been analyzed using single crystal methods, such as fullerenes, metalloporphyrins, and many other complicated compounds. Single crystal is also used in the pharmaceutical industry, due to recent problems with polymorphs. The major limitation to the quality of single-crystal data is crystal quality, these crystals are usually obtained by recrystallization.

Inorganic single-crystal x-ray crystallography is commonly known as small molecule crystallography, as opposed to macromolecular crystallography.

[edit] Powder Diffraction

Main article: Powder diffraction

X-ray powder diffraction finds frequent use in materials science because sample preparation is relatively easy and the test itself is often rapid and non-destructive. The vast majority of engineering materials are crystalline, and even those which are not yield some useful information in diffraction experiments.

The pattern of powder diffraction peaks can be used to quickly identify materials (thanks to the International Centre for Diffraction Data pattern database), and changes in peak width or position can be used to determine crystal size, purity, and texture. Since all possible crystal orientations are measured simultaneously, the diffraction pattern is observed as a series of concentric rings of varying intensity.

An X-ray diffraction image for the protein myoglobin.

[edit] Biological structures

The first solved protein crystal structure was of Sperm Whale myoglobin, as determined by Max Perutz and Sir John Cowdery Kendrew in 1958, which led to a Nobel Prize in Chemistry. The X-ray diffraction analysis of myoglobin was originally motivated by the observation of myoglobin crystals in dried pools of blood on the decks of whaling ships. Today X-ray crystallography is used by pharmaceutical companies to determine specifically how drug lead compounds interact with their protein targets. Biological X-ray crystallography is to date the most prolific discipline within the area of structural biology; out of the ~42000 protein structures solved, X-ray crystallography is responsible for ~36000. NMR spectroscopy has contributed almost 6000 and electron microscopy just over 140. Other biophysical methods, such as IR spectroscopy and powder diffraction make up the remaining structures, according to the Protein Data Bank (PDB).^[1]

[edit] Crystallization

In order to solve the three-dimensional structure of a molecule, it must first be crystallized (see also recrystallize). This is because a single molecule in solution has insufficient scattering power alone, and the scattering of multiple molecules in a concentrated solution is too convoluted to yield high resolution information (see Small angle X-ray scattering (SAXS)). A crystal can be considered to be an (effectively) infinite repeating array of the molecule of interest. The Laue conditions and Bragg's law show that constructive interference between diffracted X-rays that are in-phase reinforce each other, so that the diffraction pattern becomes detectable. The geometric conditions where diffraction occurs can be visualised using Ewald's sphere.

Crystallization of small molecules has traditionally followed three methods

• Diffusion gradient- solubility or temperature
• Concentration through evaporation
• Sublimation (not recommended due to low-quality crystals).

Even though small molecules are relatively more facile to crystallize than macromolecules, there are many compounds reported that have failed to give diffraction quality crystals.

Crystallisation of macromolecules is not trivial. Traditional methods of crystallising inorganic molecules have been modified to be gentle enough for proteins, which are sensitive to temperature and high concentrations of organic solvents. Many methods exist to crystallise proteins, but the two most successful methods are the microbatch and vapour diffusion techniques. Concentrated solutions of the protein are mixed with various solutions, which typically consist of:

• a buffer to control the pH of the experiment
• a precipitating agent, to induce supersaturation (typically polyethylene glycols, salts such as ammonium sulphate, or organic alcohols).
• other salts or additives, such as detergents or molecule co-factors

In either microbatch or vapour diffusion, the protein solutions are allowed to concentrate over time. A common method for crystallisation is hanging drop vapour diffusion technique. A small droplet of concentrated protein- and precipitant-containing solution is applied to a glass coverslip that is then inverted. The droplet is suspended above a larger reservoir of a similar solution lacking protein but containing a higher concentration of precipitant. A closed environment is formed containing the suspended droplet and reservoir. Over time, the droplet containing protein equilibrates with the larger reservoir beneath it as volatile water in the droplet transfers to the reservoir, effectively increasing the precipitant concentration in the protein droplet. In solutions of a favourable composition, the protein becomes supersaturated and crystal nuclei form, leading to crystal growth. This is the optimal outcome. Otherwise (and typically) the protein forms a useless and amorphous mass as protein precipitates out of solution. Typically protein crystallographers can screen hundreds or thousands of conditions before a suitable condition is found that leads to a crystal of suitable quality. As a rule of thumb, some useful structural detail can be gained from a crystal that diffracts with a resolution of better than 4 ångströms (400 picometers).

Many biomolecules of interest still have not been successfully crystallised. Imperfections in the crystal structure, caused by impurities, sample contamination, or multiple stable conformations of the subject protein can prevent the acquisition of atomic resolution images. Convection caused by temperature variations within the forming crystal can also cause imperfections, and one of the proposed scientific applications of the International Space Station is the growth of crystals, because convection is reduced in the free fall environment of an orbiting spacecraft.

[edit] Single-crystal X-ray diffraction experiment

Once prepared, the crystals are harvested and then 'mounted'. Several methods of mounting exist: it is possible to hold the crystal in a thin glass tube using grease or by using superglue or epoxy resin to hold the crystal to a glass fibre. A modern alternative is to use a drop of oil and liquid nitrogen to fix the crystal to the fibre. By cooling crystals the radiation damage incurred during data collection is reduced and decreases thermal motion within the crystal, giving rise to better diffraction limits and higher quality data.

Crystals are then mounted on a diffractometer coupled with a machine that emits a beam of X-rays. This can either be a sealed X-ray tube with a stationary anode (circa 2 kW DC input), a rotating-anode type source (circa 14 kW DC input) or a synchrotron (much higher photon flux). The X-rays are diffracted by their interaction with the electrons in the crystal, and the pattern of diffraction is recorded on film or more recently charge-coupled device detectors and scanned into a computer. Successive images are recorded as a crystal is rotated within the X-ray beam.

Before the advent of cryocooling, all data was collected at room temperature. Increased radiation damage to the crystal meant that sometimes several crystals had to be used to obtain a single dataset. Cryocooling has reduced this problem. Moreover, instead of collecting the data spots one at a time, many modern machines use an array of X-ray detectors (a CCD array) to collect data over a large range of angles at once.

[edit] Data processing

A representation of the 3D structure of myoglobin, showing coloured alpha helices. This protein was the first to have its structure solved by X-ray crystallography by Max Perutz and Sir John Cowdery Kendrew in 1958, which led to their receiving a Nobel Prize in Chemistry.

The data collected from a diffraction experiment is a reciprocal space representation of the crystal lattice. The position of each diffraction 'spot' is governed by the size and shape of the unit cell, and the inherent symmetry within the crystal. The intensity of each diffraction 'spot' is recorded, and is proportional to the square root of the structure factor amplitude. The structure factor is a complex number containing information relating to both the amplitude and phase of a wave. In order to obtain an interpretable electron density map, phase estimates must be obtained (an electron density map allows a crystallographer to build a starting model of the molecule). This is known as the phase problem, and can be solved in a variety of ways:

• Molecular replacement - if a structure exists of a related protein, it can be used as a search model in molecular replacement to determine the orientation and position of the molecules within the unit cell. The phases obtained this way can be used to generate electron density maps.
• Heavy atom methods - If high-molecular weight atoms (not usually found in proteins) can be soaked into the crystal, direct methods or Patterson-space methods can be used to determine their location and to obtain initial phases.
• Ab Initio phasing - if high resolution data exists (better than 1.6 angstrom or 160 picometers) direct methods can be used to obtain phase information.

Having obtained initial phases, an initial model (the hypothesis) can be built. The Cartesian coordinates of atoms and their respective Debye-Waller factors (accounting for the thermal motion of the atom) can then be refined to best fit the observed diffraction data. This generates a new (and hopefully more accurate) set of phases and a new electron density map is generated. The model is then revised and updated by the crystallographer and a further round of refinement is carried out. This continues until the correlation between the diffraction data and the model is maximised.

Once the model of a molecule's structure has been finalised, it is often deposited in a crystallographic database such as the Protein Data Bank (for protein structures) or the Cambridge Structure Database (for small molecules). Many structures obtained in private commercial ventures to crystallise medicinally relevant proteins, are not deposited in public crystallographic databases.

[edit] See also

Wikibooks has a book on the topic of

Xray Crystallography

• Neutron diffraction
• Wide angle X-ray scattering (WAXS)
• Small angle X-ray scattering (SAXS)
• Bragg's law
• Bravais lattice
• Crystallographic point groups
• Crystal structure
• Dynamical theory of diffraction
• Diffractometer
• Fourier transform
• Dorothy Crowfoot Hodgkin
• Molecular modeling
• Patterson function
• Reciprocal space
• Phase problem
• Powder diffraction
• Space group
• Electron diffraction
• X-ray diffraction

[edit] Bibliography

• Ewald, P. P., editor 50 Years of X-Ray Diffraction (Reprinted in pdf format for the IUCr XVIII Congress, Glasgow, Scotland, Copyright © 1962, 1999 International Union of Crystallography).

[edit] References

1. ^ [1]

• Drenth J. Principles of Protein X-Ray Crystallography. Springer-Verlag Inc. NY: 1999, ISBN 0-387-98587-5.
• Glusker JP, Lewis M, Rossi M. Crystal Structure Analysis for Chemists and Biologists. VCH Publishers. NY:1994, ISBN 0-471-18543-4.
• Rhodes G. Crystallography Made Crystal Clear. Academic Press. CA: 2000, ISBN 0-12-587072-8.
• "Small Molecule Crystalization" (PDF) at Illinois Institute of Technology website