# Principles of Protein Structure Assignment 1996

## A Short Primer on X-ray Crystallography

Consider light of a single wavelength passing through a thin plate of glass with parallel lines etched into it. If the line spacing is of the same order of magnitude as the wavelength of the light then when the rays are scattered from the lines, they will constructively interfere in some directions and destructively interfere in others. The scattered (diffracted) waves give rise to a characteristic pattern of alternating light and dark fringes (different orders of diffraction) on a screen placed in front of the glass. By measuring the angular location of the fringes, and knowing the distance to the screen and the wavelength of the light it is possible to work out the line spacing on the etched glass (diffraction grating) using Bragg's equation. The order (n) of the fringe (constructive interference from waves arriving one, two , three .... wavelengths out of phase) is simply its position in the fringe pattern.

Now consider a protein crystal replacing the diffraction grating above. Because the protein repeats periodically in the crystal, a particular atom in each protein layer lies on a plane through that layer. At different orientations to the incident light, when the crystal is rotated on its three cartesian axes, different planes (this time across many protein layers) containing the same atom will diffract (albeit more weakly). In principle it should be possible to obtain diffraction from all the layers in the crystal and determine their spacing from the resulting diffraction pattern. Because an object will only diffract light with a wavelength similar to the size of that object, Max von Laue (a German physicist) realised in 1912 that X-rays, which have wavelengths similar in size to the spaces between atoms in a crystal, could be used to reconstruct the atomic coordinates within the crystal.

Because the crystal is rotated on its axes, the diffraction pattern is no longer a set of fringes but is now a pattern of symmetrical spots. It is no longer possible to tell which order of diffraction gives rise to which spot i.e. the phase information is lost and an unambiguous plane separation giving rise to that spot cannot be determined.

The phase problem can be solved if the two similar compounds, differing only by a subsitution (or addition or subtraction) of a single atom, can be separately crystallized with the same unit cell. In this isomorphous ("same form" in Greek) replacement method the diffraction patterns from the two crystals are identical but have progressively different intensities attributable to the different scattering power of the switched atom. These diffences allow the phase of each spot to be determined.

The isomorphous replacement method was first used by Bragg to determine the structure of crystals of common salt (by comparing the diffraction pattern from sodium chloride with that of potassium chloride). In 1962, Max Perutz received a Nobel prize for determining the crystal structure of haemoglobin by comparing its diffraction pattern with that of an isomorphous derivative containing mercury (which attached to the free sulphydryl group on each half molecule; it did not replace the iron as one might think!).

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Last updated 2nd Apr '96