SIZE, SHAPE, AND HYDRATION OF VIRUSES 4o 



value of vim. Now mFo is the actual volume of the particle, so 



y — V m 

 V — mV is the associated volume of water. Then ' or 



m 



— — Fo, is the mass of water per gram of anhydrous virus, the 



conventional method of expressing degree of hydration. This 

 ratio is denoted by r. 



This method is well exemplified by the work of Miller and 

 Price (1946) on southern bean mosaic virus. Their results are 



shown in Fig. 2.6. The measured values for — — 1 are plotted 



against C, the gram concentration of virus. The points fit a 

 straight line quite well, so that Einstein's relation is obeyed. 

 In these studies, the virus was purified by chemical precipi- 

 tation and by ultracentrifugation, and viscosity determinations 

 were made for each. The agreement is very satisfying. 



From the slope of the line, is found to be 1.76 and so V /m 

 is 1.76. Pycnometric measurements give the unhydrated partial 

 specific volume as 0.70, so the mass of water per gram of an- 

 hydrous virus is found to be 1.06. 



Asymmetric Particles 



The pleasantness and simplicity of working with spherical 

 particles ceases to hold if the viruses are rod shaped and becomes 

 unmanageable if some description in terms of ellipsoids is not 

 applicable. This doesn't mean that queer shapes do not diffuse 

 and sediment in a regular way, but that measurements do not 

 tell us their shape. Virus work is still at an early enough stage 

 so that we are content to take any information and add it up. 

 Nevertheless, the sedimentation of phage-shaped particles is 

 not a powerful way of studying their form. 



The central point to study is clearly the viscous flow of odd 

 shapes. Neither the centrifugal reaction forces nor the "os- 

 motic" forces which apply in sedimentation and diffusion are 

 dependent on shape, but the viscous drag does definitely depend 

 on shape. The problem of viscous drag experienced by ellipsoids 

 was solved by Gans (1928). Ellipsoids permit precise solutions 



