THE SIZE AND SHAPE OF VIRUSES I9 



D = SI 



Nf 17) 



D Is the diffusion constant, H, the gas constant, N, Avagadro's number, and T 

 the absolute temperature. For the unhydrated sphere, according to Stoke 's 

 law, f = StfTT) ; therefore, 



D _ RT 



~ etr-^Nr (8) 



Thus the radius of an unhydrated sphere can be calculated from the diffusion 

 constant. Then the molecular weight can be determined from the value for the 

 radius and the density. Diffusion studies on bushy stunt virus were carried 

 out by Neurath and Cooper. A value for D of 1.15 x 10"'7 cm.* /sec. was ob- 

 tained. When this value is considered in conjunction with the value of I.36 

 for the dry density of the virus, one obtains about 19 x 109 for the molecular 

 weight. 'I'his does not agree at all with the value 7«^ x 10", calculated from 

 sedimentation data. Obviously, something Is wrong with the assumption that the 

 bushy stunt virus particle is an unhydrated sphere. However, it Is not neces- 

 sary to make assumptions concerning the shape and the state of hydration of the 

 virus particles in order to determine the molecular weight. This Is true be- 

 cause the same friction factor which determines the rate of sedimentation of a 

 virus also determines the rate of diffusion. Hence, by combining equations (4 J 

 and (7)» the friction factor, f, can be eliminated entirely, and the particle 

 weight can be expressed as a function of the sedimentation and the diffusion 

 constant. 



D V 8 ^ (9) 



Since mg = mp ££ and Nmp= M, where M Is the molecular weight, 



RT ^ 1 / da \ . or M = RTs 



110} 



In the diffusion constant, 1.15 x 10~7, is used in conjunction with the sedi- 

 mentation constant, ,132 x 10"l3, in equation (10), a value for the molecular 

 weight of 10.6 X 10° is obtained. The error has been estimated as + 1,000,000. 

 This is the true value of the anhydrous molecular weight. In order to explain 

 the discrepancy between the value calculated from diffusion data and that cal- 

 culated from sedimentation data, one would have to assume either that the par- 

 ticles are not spherical, or that they are hydrated spheres which have soaked 

 up 77^ of their own weight of water. Since we know that the particles are es- 

 sentially spherical, we are forced to the conclusion that they are hydrated 

 spheres . 



X-ray diffraction studies have been made on crystals of bushy stunt virus 

 by iiemal, Fankuchen and Riley. Because the crystals were too small to be ex- 

 amined singly, these workers studied powder diagrams obtained from suspensions 

 of the crystals in their mother liquor, yrom these studies, they decided that 

 the crystal structure consists of a face-centered cubic lattice, that there are 

 two virus molecules per unit cell, and that the wet molecular weight Is 22 mil- 

 lion. *et crystals shrink about 20% when dried In a vacuum. This ahrlnkage 

 was verified by the decrease in the interplsmar distances within the crystals, 

 as measured by X-ray technique. From these considerations alone, it can be com- 

 puted that in the wet crystals each gram of virus is associated with. 67 grams 



A. 



