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



Pauling realized that this was a mistake. Pauling and Corey demon- 

 strated that a helix with 3.7 amino acid residues per turn, a diameter of 

 6.8 A and turns spaced 5.4 A apart would be permitted by the observed 

 bond angles. This is shown in Figure 9 for a right-handed helix. 

 Left-handed a-helices are also possible. However, the diffraction 

 pattern for X rays due to such a helical structure was more complex 



than that for any of the simpler models. 

 Cochran, Crick, and Vand carried 

 out a theoretical study of the pre- 

 dicted X-ray pattern for helical struc- 

 tures. They showed that it was 

 necessary to orient the X-ray beam 

 at an oblique angle to the fibers. In 

 general, the helical structures lead 

 to patterns similar to that diagrammed 

 in Figure 10. Whereas the simpler 

 molecules and crystals involved such 

 terms as cos 2-n(hx + ky + Iz + a), 

 the helical structures involved Bessel 

 functions of the distance from the 

 center of the helix. 



The a-helical structure of Pauling 

 and Corey fits very well to the 

 diffraction patterns observed for syn- 

 thetic polypeptides. It is generally 

 accepted that many natural fibrous 

 proteins occur as helices because their 

 X-ray diffraction patterns are of the 

 a-type which is similar to that of 

 Figure 10. However, many unex- 

 plained spots are present. The data 

 for the fibrous protein collagen can 



Figure 9. Thea-helix of Pauling and Corey 

 redrawn to emphasize helical polypeptide 

 chain. Dotted lines indicate hydrogen 

 bonding between = O of one turn with the 

 H — N of the turn below. This is a close- 

 packed structure. The polypeptide helix 

 has a radius of 3.4 A and an interturn 

 distance of 5.4 A. There are 3.7 residues 

 per turn. The R groups are much larger 

 than shown; they extend as far as 10 A. 



