X-Ray Crystallography (Molecular Biology)

X-ray crystallography is still the experimental technique that determines the most detailed structures of macromolecules. In 1912 Knipping and Friedrich in Laue’s laboratory performed the first X-ray diffraction experiment with a crystal (1). Their result showed at the same time that X rays behave as waves and that crystals display a high degree of order in arranging their atoms, ions, or molecules. The crystal acts as a three-dimensional grating and diffracts X rays just as visible light is diffracted by an optical grating. Since 1912, X-ray crystallography has had an enormous impact on chemistry and biology. At first, great triumphs were obtained in the field of inorganic chemistry. The structures of simple ionic compounds and of complex structures, like the silicates, became understood, and ionic radii could be measured with high accuracy. Unlike inorganic compounds that are mainly ionic, organic compounds consist of molecules. The intensity of the beams diffracted by organic compounds is relatively low and, in the beginning, progress was slow in determining their structures. However, the introduction of improved hardware and Fourier analysis solved the problem, and now the X-ray structure determination of a small or medium-sized organic molecule is an easy job, at least when good quality crystals are grown.

Protein crystallography is the youngest branch of X-ray crystallography. It started in 1934 when Bernal took the first X-ray diffraction picture of a protein crystal (2), first a crystal of pepsin, soon followed by a crystal of insulin. These observations showed that even these large molecules are nicely ordered in their crystals and that their structures might be solved. This was not an easy problem, however, and it took twenty years to find a solution (3). Surprisingly, it could be done by a technique already successfully applied for small organic compounds: the method of isomorphous replacement in which a heavy atom is attached to the protein structure. It was Perutz’ achievement to show that the method could also be used for proteins and that the heavy atoms cause a much larger change in intensity than initially expected. Because of the rather primitive instrumentation, progress was slow at first. With the introduction of more sophisticated instrumentation and computers with suitable software, X-ray crystallography of proteins has grown to a relatively common technique, and structures are being published with ever increasing speed. They are collected in the Protein Data Bank, Brookhaven National Laboratory, Upton, NY 11973-5000, USA (see Databases).

1. X-ray sources

In the home laboratory, X rays are produced in vacuum tubes by bombarding a metal anode with accelerated electrons. They are either sealed tubes that have a static anode or they have a rotating anode and are continuously pumped. An X-ray tube emits a spectrum of wavelengths whose characteristics depend on the metal. For most diffraction experiments, a single wavelength is selected by a monochromator, 0.71 A from a molybdenum anode or 1.5418 A from a copper anode. Diffraction is stronger for the longer wavelength, and this is preferred for proteins. The maximum power of an X-ray tube is limited by heating of the anode caused by the accelerated electrons. Rotating anode tubes have better heat dissipation, produce a higher intensity beam, and therefore, are preferable for protein work.

Much stronger X-ray beams are produced in synchrotrons (4). These devices have electrically charged particles (electrons or positrons) circulating in a vacuum. A continuous spectrum of electromagnetic radiation down to a certain minimum wavelength is emitted when the particles change direction. The minimum depends on the power of the synchrotron. The higher the power, the shorter the minimum wavelength. A wavelength near 1 A is often chosen for protein crystallography with synchrotron radiation. This has the advantage over the copper wavelength of 1.5418 A that the absorption of the beam is much lower.

2. X-ray detectors

The beams diffracted by crystals of small compounds are usually detected and measured with a diffractometer. Using this instrument, the crystal can be rotated around three or four axes and can reach nearly every orientation. The diffracted beams are measured with a photon counter. Because the beams are measured one after the other, this process is slow and not very suitable for protein crystals where thousands of beams must be measured. Protein crystallographers prefer an instrument that has one or more axes to orient the crystal and is equipped with an area detector on which hundreds or thousands of diffracted beams are registered nearly simultaneously. A popular type is the imaging plate covered with phosphorescent material. After registration, the information collected on the imaging plate is released by a laser and read with a photomultiplier.

3. Diffraction theory

The most convenient way to understand the diffraction of X-rays by a crystal was introduced by Bragg (5). It is based on the idea of the reflection of X rays from lattice planes in the crystal (see Bragg Angle). They are the planes constructed through the lattice points, which are the corners of the unit cells. Within a set, the planes are parallel and equidistant, and have a perpendicular distance d. Such a set is characterized by three indices: /?, k, and The beams reflected at an angle q from the lattice planes reinforce each other only if the path difference for beams from successive planes is equal to a whole number of wavelengths. This occurs when Bragg’s law is fulfilled:

The reflected beams have the same indices /?, k, and ^as the set of planes from which they are reflected. Bragg’s law gives the direction of the diffracted beams, but not their intensity. The latter is determined by the distribution of atoms and molecules in the unit cell of the crystal. It can be shown that Bragg’s reflection idea is equivalent to positive interference of the scattering by the individual unit cells in the crystal. The scattering by the unit cells is reinforced in the Bragg directions and extinguished in other directions.

In powder diffraction, the specimen is not a single crystal but consists of a large number of crystal grains. It is exposed to a parallel beam of X rays, and there are always some grains for which the Bragg condition is satisfied. The result is a series of circles centered around the direct beam. The powder method is suitable only for very simple structures, where only a limited number of data are sufficient for the structural determination and for detecting phase transitions. It is completely useless for proteins.

When X rays interact with a crystal, they are scattered by the electrons in the crystal. A unit cell contains a huge number of electrons, and every electron scatters the X-ray beam. These beams interfere with each other, and the net amplitude of the scattering by a unit cell corresponds to a number of electrons F, which is smaller than the total number of electrons in the unit cell and depends on the electron distribution in the unit cell. Because the crystal scatters only if the beams originating from the individual unit cells positively interfere, the amplitude of the scattered beam hkt is proportional to F {hkt), the scattering by one unit cell. This is the amplitude of the vector F {hkt). It can be derived that

where F (hkt) is called the structure factor for reflection (hkt). It can be regarded as a vector with amplitude F and phase angle a: F = l< exp [7 a]; x, y and z are fractional coordinates along the unit cell axes a, b, and c; V is the volume of the unit cell and r the electron density distribution in the cell. Using Eq. (2), the scattering by the crystal can be calculated from the electron distribution in the unit cell. In the reverse direction, r(xyz ) is derived from the F( hkl) ‘s of all scattered beams. This is accomplished by applying a mathematical procedure called Fourier transformation. If Eq. (2) is true, then it is also true that

using Eq. (3), the electron distribution in the unit cell can be calculated provided that the values of F (hkt) and a (hkt) are known for all reflections. The F(hkt) ‘s are easily found because, apart from correction factors, they are proportional to the square root of the scattered intensities I (hkt). The phase angles a( hkt) cannot be measured, however (see Phase Problem), but must be derived indirectly by one of these four methods:

1. direct methods

2. isomorphous replacement

3. molecular replacement

4. MAD, multiple wavelength anomalous dispersion

Direct methods are the method of choice for small compounds, but they are not yet sufficiently developed for macromolecules. The other three methods are applicable to large molecules.

The degree of detail in the electron density map calculated with Eq. (3) depends on the number of reflections included in the summation. The greater the number, the greater the accuracy. The greater the volume of reciprocal space included, corresponding to reflections from smaller spacings in the crystal, the greater the atomic detail in the electron density map. This is the "resolution" that is always quoted with every structure determination by X-ray crystallography.