VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 213 



hydrogen can reattach one to increase the local positive charge. In 

 the ordinary way, there are many of these groups and not a 

 great deal of reason why one should have hydrogen attached to 

 it, rather than another. The charged groups produce dipole mo- 

 ments which, on the whole, average to a small value, but which 

 can, by fluctuations in the positions of the attached protons, 

 cause quite large mean-square dipole moments. Kirkwood and 

 Shumaker (1952) have pointed out that such fluctuating dipoles 

 can influence the migration of protons in a second protein mole- 

 cule and thus induce dipoles which are attracted to the first 

 molecule. If one were constructing a large-scale model to illus- 

 trate the nature of the London-Van der Waals forces, this would 

 serve very well , the reason for the fluctuations is totally different, 

 and the factors influencing their size are also quite different, but 

 the net effect of producing attraction is the same. 



The theory developed by Kirkwood and Shumaker can be used 

 to explain the fact that small concentrations of protein in solu- 

 tion produce a large change in dielectric constant, a fact which 

 was previously ascribed to the presence of large, permanent (or 

 nearly so) dipole moments. If, instead of such moments, there is 

 supposed to be a lability of the protons which are attached to the 

 kind of groups just described, then the influence of an external 

 electric field will be to modify the proton distribution and bring 

 forth induced dipoles, which are large, on the average, and so 

 cause an increase in the dielectric constant. For the four proteins 

 jS-lactoglobulin, ovalbumin, hemoglobin, and serum albumin, the 

 mean-square dipole moment found experimentally agrees quite 

 well with the theoretical predictions. 



In view of this fact, the value for the interaction energy be- 

 tween protein molecules calculated by the same authors is of 

 considerable interest. If Lis the interaction energy 



^ (A7i)MA^)2 



^K^h^kT 



where (Agi)" and (Ag^)^ are the average, total charge fluctuations 

 of the two molecules. The energy falls off as 1/R^, which is very 



