54 YOS, BADE AND JEHLE 



their corresponding side groups come to lie just between the hehxes in such a 

 way that pairs of identical sidegroups belonging to the two identical protein 

 helixes, respectively, come to lie essentially on top of each other, so that the two 

 proteins interlock with corresponding sidegroups clinging together. The mutual 

 orientations of these pairs of identical sidegroups is the advantageous one ac- 

 cording to equation (12). Even if the polarizabilities are not extra strong, the 

 specificity may become very high due to the matching pattern of pairwise 

 identical sidegroups. Intervening spaces are expected to be filled, in a statisti- 

 cal fashion, by small molecules and ions from the medium. 



As the association (and proper orientation) between mirror molecules fails 

 in the general case because of permanent dipole contributions, a laevo structure 

 will duplicate a laevo, not a dextro structure in accordance with the behavior 

 of macromolecules in living organisms (Haldane, 1937; Oparin, 1938). 



The problem of differentiation, in particular in the early development and 

 growth of a fertilized egg, might also be related to the rearrangement free 

 energies of the type considered here (Weiss, 1949, 1951, 1953, 1955). 



With regard to the properties of the London force, molecules are identical if 

 they have the same distribution of polarizabilities. Structural identity is a 

 sufficient but not a necessary condition for the "identity" on which London 

 force specificity depends. Correspondingly London specificity may play a role 

 in a wider group of biological specificity phenomena such as enzyme specificity 

 or antigen antibody specificity. 



Before studying the biological implications of the London force it would be 

 appropriate to pursue the question whether the specificity theorem sheds light 

 on the problems of crystal formation, particularly that of van der Waals crys- 

 tals. One may consider the case of a van der Waals crystal surrounded by a 

 medium composed not only of that particular molecule but of others too, mole- 

 cules which differ from the one of the crystal only by their polarizability dis- 

 tribution. Attachment of one more molecule to a crystal of its likes implies 

 one of several quadruplet terms A4.4i „ as a free energy change. In most 

 crystallization processes, however, the molecules (or atoms) about to crystal- 

 lize are not prevented from approaching each other closely; therefore all kinds of 

 bonds come into play which were disregarded in the cases discussed in this note. 

 Nevertheless (and particularly in certain molecular crystals and virus crystals, 

 (Wyckoff, 1949, 1951; Wyckoff and Labaw, 1955)) the quadruplet expres- 

 sions of London forces may come into the picture. The quadruplet formulation 

 may be used for any sort of additive forces. 



In order to give an idea about the kinds of orientation problems which come 

 up in the formation of macromolecular arrays, the problem of orientation 

 preferences is singled out in the following by discussion of a particular case: 

 crystallization of perfectly globular molecules, all identical molecules whose 

 polarizability distributions for the various frequency ranges are highly aniso- 



