212 THE PHYSICS OF VIRUSES 





2 , 1 _ 2 



rf2 + {d + yY ~ {d+yl<iy\ 



where A^ is the number of atoms per unit volume of the plane 

 material, and B is the constant in the relation for the potential 

 energy of two atoms. 



In the case of two spheres, radius a, placed so that the shortest 

 distance between their surfaces is //, we can use the parameter 



*S = . Thus S is the ratio of the total separation of the 



centers to the diameter of one sphere. Then the resulting poten- 

 tial energy (Verwey and Overbeek, 1948, p. 160) is 



U = - 



TT 



N^B 



6 

 or, approximately, 



U = - 



+ - + In "^ 



4 ' *S2 ' ^2 



12// 



For a rough guide, we can follow Verwey and Overbeek and put 

 tt'^N^B = 10~^^ ergs, so we have 



In actual cases, the macromolecules are immersed in a medium 

 which intervenes between them. This does not, however, dimin- 

 ish the field strength except in the usual way in terms of the 

 dielectric constant. At the frequencies involved, there is no 

 opportunity for wholesale rotation of polar molecules but only 

 for the electronic adjustments in each. Thus the dielectric con- 

 stant to be used is the square of the refractive index [about 

 (H)^]- So the effect of the medium will be to modify downward, 

 by a factor of about two, the value of the interaction potential. 



Fluctuating Proton Charge Forces 



One of the characteristics of proteins is the fact that many of 

 the side chains consist of amino acids containing dissociating 

 groups. Groups such as — NH2 can attach a hydrogen ion to be- 

 come — NH3, and a group like — C00~ which has already lost a 



