286 X-ray Analyses of Proteins and Nucleic Acids / 1 5 : 5 



of the types known to be present and at reasonable distances from other 

 atoms to which they can be bonded. (The bonds can often be found by 

 the methods of classical organic chemistry.) In the final analysis, phase 

 guessing is very similar to working a crossword puzzle or solving a murder 

 mystery story, and as in these, one finds, if successful, an answer which is 

 no longer a guess. 



Various schemes have been developed for the initial-phase guessing. 

 One of the most successful involves placing a heavy atom such as I or 

 Br within the molecule. 3 The heavy atom diffracts more strongly than 

 the others, so it may be located first. To do this, Equation 2 is used, 

 setting^ to zero for all but the heavy atom. Once it is located, approxi- 

 mate values for many of the phases can be determined at once. With 

 these as a starting point, one adjusts these phases and the others to give 

 more and more sharply defined electron-density contours. The final 

 solution is an accurate determination just as in the crossword puzzle. 



For certain crystals, the unit cell is symmetric about the center and, 

 therefore, it can be shown that all the a^'s have the value or n. 

 These are only two choices, but if 100 points are used there are 2 100 or 

 about 10 30 possible sets of guesses. By the use of heavy-atom substitu- 

 tion, this hopelessly large number may be reduced to a mere few billion. 

 Protein and nucleic acid crystals are not even symmetric about the center 

 of the unit cell, so that the problem is more difficult when using these 

 molecules. 



The entire adjustment of phase values and recomputing the F's and 

 p is a lengthy, tedious process. With an electrical desk calculator and 

 a protein crystal, this would take many human lifetimes. With electronic 

 computers, it has been possible to find the details of the structural 

 arrangements of the atoms within many smaller biological molecules 

 (molecular weight < 2,000) . The remainder of this chapter discusses 

 the contributions of the method of X-ray diffraction to the determination 

 of the structure of proteins and nucleic acids. 



5. Protein Structure 



In Chapter 8, it was mentioned that one class of proteins, the globulins, 

 could exist in either a fiberlike or a globular state. Most proteins do 

 not have these two alternatives but, rather, are only fibrous or only 

 globular. X-ray diffraction studies have been applied to both types of 

 protein structure with varying degrees of success. 



1 This technique is useful if the heavy atom does not alter the crystal structure; 

 it is called isomorphic replacement. 



