The Application of X- Ray Crystallography 

 to the Study of Biological Macromolecules 



J. C. KENDREW and M. F. PERUTZ 



A brief account is given of methods of analyzing crystal structures 

 by means of x-rays, with particular reference to their application to 

 crystals of large molecules of biological origin. Fourier and Vector 

 {Patterson) syntheses are described, and it is shown that where the 

 molecule is large there is sometimes a general resemblance between 

 some features of the vector structure and the molecular structure 

 from which it is derived. 



This paper serves as an introduction to the two which precede it, and 

 is intended as a brief conspectus of the applications of x-ray crystal- 

 lographic techniques, particularly to the study of large molecules (but 

 excluding fibrous structures), for the benefit of workers in other fields 

 who may be unfamiliar with these methods. It will not be possible in 

 the short space available to provide mathematical proof or even con- 

 vincing evidence for many of the statements made. We are trying to 

 give the reader a glimpse of the physical principles underlying the 

 different methods of analysis ; for more detailed information some of 

 the references given at the end of this paper should be consulted. 



THE STRUCTURE OF CRYSTALS 



A perfect crystal consists of a three-dimensional array of molecules 

 arranged regularly in repeating units of pattern. In two dimensions a 

 piece of patterned wallpaper is analogous ; if corresponding points in 

 the pattern (known as ' lattice points ') are joined by two sets of 

 parallel lines the wallpaper is divided into ' unit cells ' of identical size, 

 shape, and contents. These unit cells are the smallest and therefore 

 the fundamental units of pattern, and in the three-dimensional array 

 they can be drawn in exactly the same way, and are defined by three 

 sets of parallel fines known as the crystal axes (denoted by a, b and c). 

 An example of a two-dimensional pattern is shown in Figure 1. 



An array of a large number of unit cells is known as the space lattice, 

 and the shape of the unit cell determines the crystal system to which 

 the crystal belongs ; seven such systems are possible, ranging from 

 triclinic (with three unequal axes and no right angles), through mono- 

 clinic (three unequal axes, two angles of 90°, one angle not 90°), 

 orthorhombic (three unequal axes at right angles), hexagonal (two 

 equal axes at 120°, the third at right angles to the first two and 



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