90 METHODS FOR DETERMINING MOLECULAR SIZE AND SHAPE 



It should be remembered that this, evidence concerns only bacterial 

 DNA. It is possible that bacteria which have no nucleus of the con- 

 ventional type (there is no nuclear membrane and no evidence for 

 mitosis) are a special case. Students should be cautious in extrapolating 

 this result to all organisms. 



THE MATHEMATICS OF THE SEDIMENTATION VELOCITY METHOD 



Quantitative data are most frequently obtained by the use of the sedi- 

 mentation velocity method. The essential features of the calculation may 

 be derived from an analysis of the forces involved. 



If a centrifugal force acts on a particle in solution, the particle will 

 move if its density differs from that of the solvent. The particle will 

 speed up but, in accelerating, the frictional resistance will be increased 

 because (for low speeds) the resisting force is proportional to the particle 

 speed. Thus the particle will accelerate until the radially outward cen- 

 trifugal force is just balanced by the radially inward frictional force. 

 From that point on the particle will move with constant speed outward, 

 since there is no net force acting on it. This force equilibrium point may 

 be written as 



F c = F r , 



where F c is the net centrifugal force and F r is the resistance force. As 

 already mentioned, F r is proportional to the velocity v. 



Fr = fv, 



where / is the proportionality constant which is known as the friction 

 coefficient. 



The centrifugal force is given by F c = mv 2 /r = mo) 2 r, where m is the 

 effective mass of a particle spinning at a rate of u> radians per second at 

 a distance r from the axis of rotation. The effective mass is the difference 

 between the mass of the particle and the mass of an equal volume of 

 solvent liquid (if the particle had the same density as the solvent liquid, 

 there would be no resultant motion) : 



4-1) 



m = m p - triL = m p 11 - I = m 



where d is the density, and the ratio of, the masses is replaced by the 

 equivalent ratio of the densities. The force equilibrium condition may 

 now be written as 



m p (l - d L /d p )u) 2 r = fv 



