15:4/ X-ray Analyses of Proteins and Nucleic Acids 281 



can best be investigated by their X-ray diffraction patterns. The 

 helical structures of crystalline and fibrous proteins and of the genetic 

 material, DNA, have been established from their diffraction of X rays. 



The resolving power of an X-ray diffraction apparatus is much 

 greater than that of a light microscope. In the light microscope, the 

 limit of resolution is set by the wavelength of incident light employed. 

 With X-ray diffraction patterns, no such restrictions exist. Using 

 monochromatic X rays such as the Cu-K ft2 radiation, the wavelength A 

 is 1.54 A but interatomic distances can readily be measured with an 

 error of less than 0.01 A. This can be compared with a theoretical limit 

 of resolution of 2 x 10 3 A for blue light. 



One may ask why a crystal has to be used rather than a single mole- 

 cule, if the resolving power is indeed of the order of 0.01 A whereas the 

 covalent bond lengths average about 1.5 A. Perhaps the most obvious 

 answer is that it is impossible to hold one molecule in place. In 

 addition, some of the X-ray photons will break molecular bonds. 

 Because many molecules are present, breaking a few bonds does not 

 have an appreciable effect on the average diffraction pattern. Perhaps 

 the most important advantage of a crystal is that it restricts the scattered 

 rays to a finite number of maxima, giving sharp, intense reflections. 



One of the difficulties of X-ray diffraction studies is that one ends up 

 with a photograph or graph with a number of spots of varying intensity, 

 such as that shown in Figure 5. The problem of reconstructing the 

 crystal and the spatial arrangements of the molecules from these spots 

 has a simple solution only for crystals of very simple molecules, such as 

 NaCl or H 2 0. For more complex molecules, a series of trial-and-error 

 solutions is necessary. The analysis which follows is presented in the 

 hope that those readers unfamiliar with this technique will acquire 

 some idea of the problems involved. 



Bragg showed that in treating X-ray diffraction by single crystals, 

 one may regard the atoms as making up reflecting planes. A beam of 

 X rays is shown incident on a single pair of such planes in Figure 6 

 (although there will in general be many planes for any given crystal). 

 From Figure 6, one may see that there will be a maximum in the diffrac- 

 tion pattern if, and only if 



n\ = 2d sin 6 (1) 



where n is an integer. With monochromatic X rays, one set of planes, 

 at most, will give a maximum for a given 6, and for any arbitrary 6 there 

 will probably be no maximum in the diffraction pattern. This could be 

 solved in Figure 6 by rotating the X-ray beam around the crystal or by 

 rocking the crystal about an axis perpendicular to the plane of the 

 paper. The latter alternative is more practical and is often employed. 



