CENTRIFUGATION 83 



where k is the gas constant per molecule, T is the absolute temperature, 

 7] is the viscosity of the solution, and r is the radius of the molecule. 



The temperature and viscosity of the solution are obtained by stand- 

 ard measuring instruments, so that the radius of the molecule can be 

 found if D is known. This formula holds only for spherical molecules. 

 For nonspherical molecules, as indicated in the section on centrifugation, 

 we combine data on sedimentation and diffusion to obtain the desired 

 information. 



For spherical molecules, we replace r in the formula by its equivalent 

 in terms of molecular weight, using the relationship 



M = d p V = %irr 3 d p . 



Thus the diffusion coefficient varies inversely as the cube root of the 

 molecular weight. This means that diffusion measurements are quite 

 insensitive to variations in molecular weight, so that other methods 

 should be used for more than approximate values of the molecular weight. 

 That this conclusion is borne out experimentally may be seen by looking 

 at the table given above. There we see that the diffusion coefficient 

 changes from 95 X 10~ 7 to 0.3 X 10~ 7 , while the molecular weight 

 changes from 75 to 2 X 10 8 . That is, a 300-fold change in diffusion co- 

 efficient corresponds to a 3 million-fold change in molecular weight. 



3. Centrifugation 



There is a radially directed force on a particle which moves along a 

 curved path. If the particle is within a container filled with a liquid 

 which is less dense than the particle, the particle will move radially out- 

 ward; if the liquid is more dense than the particle, the particle will float 

 inward. As indicated in Fig. 38, the important physical parameters are 



r — the radius of circulation of the particle p, 



a) — the frequency of rotation of the centrifuge tube, in radians per 



second, 

 d p — the density of the particle, and 

 d L — the density of the liquid. 



A centrifuge is a device for spinning tubes containing particles dis- 

 solved in a liquid. Centrifugation is used currently in five different ways 

 in biology. 



(a) By centrifuging a suspension of particles for a sufficiently long 

 time in a liquid that is less dense than the particles, the particles are 

 packed into a pellet at the bottom of the tube. They are then collected by 

 decanting the supernatant fluid. We say that the particles have been 

 pelleted or sedimented. 



