24 



VIRUSES 



means that any hydration of totacco mosaic virus must cause swelling in only the 

 two dimensions perpendicular to the length of the particle. iWien this fact Is 

 taken into account, it can he shown that the agreement between the dimensions 

 obtained by direct means and those computed from viscosity and sedimentation data 

 is not affected adversely. However, the agreement of the values calculated from 

 diffusion and either sedimentation or viscosity data with the value obtained by 

 direct means no longer is satisfactory. 



Stoke 's law for the friction coefficient of a spherical particle moving In 

 a viscous medium was derived for the case of a particle in an infinitely dilute 

 solution. Stoke 's law predicts that the coefficient of friction of the particle 

 is directly proportional to the viscosity of the solvent. In actual practice, 

 one always measures the movement of particles in a solution of finite concentra- 

 tion. It is necessary, then, to make a decision in applying the sedimentation 

 equation whether the viscosity of the solvent or the viscosity of the solution 

 should be utilized. It has been the custom to use the viscosity of the solvent. 

 This is the equivalent of making the assumption that the sedimenting particle 

 moves through pure solvent rather than through a solution of similar particles. 

 On the basis of such simple theoretical considerations, one might expect that 

 the sedimentation rate of a protein would be independent of the concentration of 

 protein. This, however, is not at all the case. As shown in figure 18, when 

 one measures the sedimentation rate of tobacco mosaic virus in solutions of dif- 

 ferent concentration, one finds that the sedimentation rate does depend upon the 

 concentration of the solution. 



X 



-\ir, 



I ' I ' I ' I ' I ' I ' I ' I 

 2 04 6 08 10 12 14 16 II 

 CONCENTRATION IN G /100 CC 



FIGURE 18 - RECIPROCAL 01? SEDIMENTATION RATE 

 OP TOBACCO MOSAIC VIRUS PLOTTED AS A FUNCTION OP 

 VIRUS CONCENTRATION. (M.A.Lauf f er, J. Am. Chem. 

 Soc. 66, 1195 (1944) J. 



The reciprocal of the sedimentation constant corrected to water at 20°C is plot- 

 ted against the virus concentration. A linear relationship is obtained. This 

 concentration dependence of the sedimentation rate is quite a common phenomenon. 

 It is particularly marked in the case of those materials which have a high in- 

 trinsic viscosity, such as solutions of gelatin and other proteins, and soluti- 

 ons of high polymeric natural products and synthetic materials. How, in the 

 case of the tobacco mosaic virus, it turns out that when one plots the viscosity 

 of a solution against the concentration of virus, one also obtains a linear re- 

 lationship over a considerable concentration range. This result is illustrated 

 in l!"igure 19. 



