VIRUS geni<:tics, multiplication, and physics 203 



constant A', the mutual potential energy is (4.8 X 10~^^)^/Kr 

 ergs. When r is 100 A, and for K = 80, which a])plies to water 

 for static or k)w-frequency fiekls, the ])otential energy is 

 2.9 X 10~^' erg. The energy Ix2\ which is a rei^resentative ther- 

 mal agitation energy, is 4.1 X lO^^^ erg at 800° K, or 27° C. This 

 is 14 times larger. Hence, such attractive forces are only capable 

 of providing an energy al)le to hold a second molecule in place, 

 in spite of thermal agitation, at distances of a few Angstrom 

 units or less. 



It is, however, not necessary that a field be sufHcient to ac- 

 count for a binding energy. If the field is sufficient to ])roduce 

 relatively ra])id motion in a definite direction, this can cause two 

 charges to come close enough together to ])ro(luce binding. Now 

 the electric field of a single, elementary charge in a medium of 

 dielectric constant 80, at 100 A, is 1,800 volts/cm. The measured 

 electrophoretic mobilities of proteins are such that, in a field as 

 high as this, a protein molecule can travel 100 /^/sec, or cover the 

 100 A necessary to become bound in 10~^ sec. Thus forces due to 

 free charges must be taken very seriously and probably account 

 for some of the efficiency of assembly of molecular architecture. 



The difficulty in the way of explaining the whole of the order- 

 ing of submolecular units in this way is the existence of ions in 

 the bacterial cell. Whenever a free charge exists on the surface 

 of a protein or nucleic-acid molecule, there will ra])idly result an 

 ionic atmosphere around this charge, and the consequent force 

 at a distance becomes totally different. In fact, the most likely 

 effect of the interaction of such charges and their atmospheres is 

 a repulsion. We can now consider these ionic atmospheres, or 

 double-layer forces. 



Ionic Atmosphere, or Double-Layer Forces 



For many reasons, a large molecule may either lose or gain 

 surface charge and so acquire a net positive or negative charge. 

 If this molecule now finds itself in a medium full of ions, the 

 ions of opposite sign are attracted to the molecule and there 

 results a double-layer as indicated in Fig. 8.0. The ])ositive 

 charges at the surface of the molecule attract negative ions, 



