THE SIZE AND SHAPE GW VIRUSES 



21 



FIGURE 16 - THE ARRANGEIIENT OF ROD-SHAPED PARTICLES OF TOBACCO MOSAIC 

 VIRUS IN NEEDLE-SHAPED PARACRYSTALS, ACCORDING TO VIEWS OF BERITAL AND 

 FANKUCHEN. LEFT, LONGITUDINAL DIAGRAM; RIGHT, CROSS SECTIONAL DIAGRAM. 

 (M.A.Lauffer and W.M. Stanley, Chera. Rev. 24, 303 (1939) ;. 



The minimum lateral spacing obtained with thoroughly dried virus crystals was 

 found to be 15 millimicrons. This value affords a precise estimate of the 

 msucimum diameter that the virus rods possess in the dried state. Thus, from 

 a combination of electron microscope and X-ray diffraction data, it is known 

 that the particles of the particular tobacco mosaic virus preparation under 

 study have an average length of 270 millimicrons and an average diameter of 

 15 millimicrons. Since these dimensions were obtained by straight-forward 

 methods, they can be accepted as direct measures of the size and shape of the 

 virus particles. 



This same preparation of the tobacco mosaic virus was also subjected to 

 diffusion, sedimentation, viscosity and partial specific volume studies. It 

 is a well-established fact that the molecular weight of a particle, regardless 

 of its shape, can be determined by the method of Svedberg, employing equation 

 (10), from the diffusion constant, the sedimentation constant and the i)artial 

 specific volume. From the data obtained, a value for the molecular weight of 

 tobacco mosaic virus of 31«6 million was computed. In view of present day con- 

 cepts, it is possible to interpret these data not only in terms of the mole- 

 cular weight, but also in terms of the shape of the virus particles. The 

 procedure is somewhat as follows. From the molecular weight, which has al- 

 ready been determined, and the partial specific volume, it is a simple matter 

 to compute the molecular volume, and from it, the radius that the virus parti- 

 cle would have if it were an unhydrated sphere, yrom this, by Stoke 's law, 

 the friction coefficient the particle would have if it were an unhydrated 

 sphere can be computed. In this calculation, no unwarranted assumption is 

 made. Thus, one can regard the value of the friction coefficient of the hy- 

 pothetical unhydrated sphere as an experimentally determined value. Uy using 

 the Einstein-Sutherland equation, which has also been subjected to experiment- 

 al verification in numerous cases, it is possible to determine directly the 

 true friction coefficient of the particle. In the case of the tobacco mosaic 

 virus under consideration, the actual coefficient of friction turned out to 

 ^e 7.6 X 10-7 grams per second, and that which the particle would have v/ere 

 it an unhydrated sphere turned out to be 3,8 x 10^ grsims per sec- 



ond. When the former is divided by the latter, one obtains a value 



of 2.0 for the friction ratio of the particle. Jj'rom an extension of the theo- 

 retical considerations used by Stokes for calculating the coefficient of 

 friction of a spherical particle. Cans, Herzog and finally Perrin contributed 

 to the development of equations which relate the friction ratio to the shape 

 of the particles. These investigators assumed that rod-like or plate-like 

 particles have shapes which can be represented by elongated or flattened 

 ellipsoids of revolution. The equations obtained show the relation between 

 the friction ratio and the ratio of the long to the short semi-axes of the 

 ellipsoids of revolution. Entirely different equations are obtained for rod- 

 like and plate-like particles. However, if independent evidence is available 

 to guide one in his choice of a rod-like or plate-like model, one can calculate 



