X-ray crystallography

X-ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of X-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice. This generally leads to an understanding of the material and molecular structure of a substance. 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 which physically interact with the incoming X-ray photons. 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. X-ray diffraction is commonly carried out using single crystals of a material, but if these are not available, microcrystalline powdered samples may also be used, although this requires different equipment, gives less information, and is much less straightforward.

Inorganic & simple organic structures

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

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 pharmaceutical industry, due to recent problems with polymorphs. The major limitation to the quality of single-crystal data is crystal quality.

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

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 JCPDS pattern database), and changes in peak width or position can be used to determine crystal size, purity, and texture.

Biological structures

The first 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 ~35000 protein structures solved, X-ray crystallography is responsible for ~29000. NMR spectroscopy has contributed almost 5000 and electron microscopy just over 100. Other Biophysical methods, such as IR spectroscopy and powder diffraction make up the remaining structures, according to the Protein Data Bank (PDB).

Crystallisation

In order to solve a crystal structure, you must first crystallise the compound of interest. This is because a single molecule in solution has insufficient scattering power alone. A crystal can be considered to be an (effectively) infinite repeating array of our 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 Poly ethylene glycols, Salts such as Ammonium sulphate or organic alcohols).
- other salts or additives, such as detergents or co-factors

In either microbatch or vapour diffusion the solutions are allowed to concentrate over time. In solutions of a favourable composition, the protein becomes supersaturated and crystal nuclei form, leading to crystal growth. 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 detail can be gained from a crystal that diffracts with a resolution of better than 4 angstroms (400 picometers).

Many biomolecules of interest still have not been successfully crystallised. Imperfections in the crystal structure, caused by impurities or sample contamination 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.

X-ray Diffraction Experiment

Once prepared the crystals are harvested and often cryocooled with gaseous or liquid nitrogen at a temperature of around 100 kelvins or -172 °C. Liquid helium is occasionally used too, but it is often not necessary to cool crystals that much (and it also costs more). Cryocooling crystals both reduces radiation damage incurred during data collection 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 rotating-anode type source or a synchrotron. 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.

Data processing

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 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, we must first obtain phase estimates (An electron density map allows a crystallographer to build a starting model of our molecule) This is known as the phase problem can be accomplished in a variety of ways.

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

Having obtained initial phases we can build an initial model (our hypothesis) and then refine the Cartesian coordinates of atoms and their respective B-factors (relating to the thermal motion of the atom) 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 Databank or the Cambridge Structure Database. Many structures obtained in private commercial ventures to crystallise medicinally relevant proteins, are not deposited in public crystallographic databases.

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