THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 285 



X-ray spots; in the extreme case the intensities are due primarily to this 

 atom. The position of the target atom can be estimated from a Patterson 

 summation, since its position will be indicated by especially prominent 

 vector peaks. In favourable cases its position can be inferred from stereo- 

 chemical considerations. When once the place of the heavy atom in the unit 

 cell is approximately ascertained, its effects upon the intensities of the X-ray 

 spots helps to clarify the determination of the phase relations of all spots. 

 The method of isomorphous replacement is especially powerful in that, if 

 more than two different kinds of heavy atoms can be found for replacement, 

 the estimates of the phase relations of the structure amplitude terms are 

 more strictly constrained by the multiplicity of conditions imposed upon 

 them. The recent success of Kendrew and colleagues (1958) in the use of the 

 method of isomorphous replacement for the analysis of the structure of 

 myoglobm makes it appear that similar methods will prove useful for the 

 spherical viruses. 



In actual practice the analysis of complex structures by X-ray diffraction 

 is by no means as mathematically straightforward as the foregoing discussion 

 might imply. The crystallographer leans heavily on all the subsidiary 

 evidence that he can find and apply. Consideration is taken of the spatial 

 requirements of atoms, of their bond distances and angles, of the require- 

 ments for structural stability, and of the types of atomic coordination likely 

 to be encountered. Considerable use is made of successive approximations — 

 a Patterson summation will suggest certain spatial parameters for the elec- 

 tron density peaks; these are used to obtain tentative two-dimensional pro- 

 jections of the true electron density; inconsistencies in the Flj.i values cal- 

 culated from these positions, as compared with observed intensities, will 

 suggest their further refinement, etc. But the final test must always be that 

 the proposed model makes stereochemical sense, and that calculated 

 intensities of the X-ray spots agree reasonably well with the measured 

 ones. 



It is premature to expect that any virus crystal has been structurally 

 analyzed to a degree that even begins to designate the atomic positions. 

 This may not even be anticipated until considerably more is known about 

 the chemical structure of viruses, because the scattering power of carbon, 

 nitrogen, and oxygen are so similar that X-ray analysis caimot distinguish 

 among them. The complete three-dimensional atomic positioning (except for 

 the hydrogen atoms) has been achieved for vitamin B^a (Hodgkin et al., 

 1956), but only with the aid of exhaustive chemical information. As will be 

 seen in more detail later, some evidence of structural detail at the level of 

 large atomic groups has been obtained for tobacco mosaic virus, but for the 

 few spherical viruses examined only intimations of internal structures have 

 been secured. Notions of sizes and molecular weights of some viruses have 



