12 MACROMOLECULAR COMPLEXES 



all the caseins reveals a high-occurrence frequency for the larger 

 non-polar amino acids. 



The tts-k-complex, although it exists at all temperatures between 

 0° and 37° C, is unstable at the lower temperatures. This is ap- 

 parent from the results obtained on adding calcium to give 0.05M. 

 At the higher temperature, the complexes are stabilized and will 

 now engage in further aggregation among themselves and with 

 /3-casein to form colloidal micelles typical of milk. Once formed, the 

 Ca-tts-k-casein complex is unusually stable to heat, changes in pH, 

 etc. We propose for it a structure in which the three as-casein mole- 

 cules are oriented axially around a k-casein molecule. At higher 

 temperatures, secondary valence interactions hold (against electro- 

 static repulsion ) the a^-casein molecules in positions such that pairs 

 of phosphorus groups attached to adjacent cts-casein monomers are 

 in juxtaposition and can be linked through the introduction of a 

 calcium ion. The precision with which the phosphate groups are 

 positioned is probably dependent upon the conformations of the 

 interactants, for, at lower temperatures, the instabilitv of the com- 

 plex suggests that the phosphorus groups cannot be cross-linked 

 b\' calcium. If each phosphorus is able to accept a calcium ion, 

 stabilization through Ca-phosphate cross-linking would be absent, 

 and, since Ca-as-caseinate is relatively insoluble at low tempera- 

 tures, it would precipitate and thus lead to a dissociation of com- 

 plexes. 



Long-Range Interactions 



The presence of large amounts of water in certain types of bio- 

 logical systems poses special problems, particularly if the condensed 

 regions of the system in question do not form a continuous network. 

 Two items currently of great interest are the structure of water in 

 such regions and the possil)ility that long-range forces ma\- be in- 

 volved in establishing the structure of the system. 



The last two items of Table 1 relate to long-range forces. The 

 first of these, listed as London-van der Waals forces, have their 

 origins in mutual polarization, as was stated above. However, the 

 specification that large planes of atoms are interacting with each 

 other, and the fact that these interactions are additive, modifies the 

 variation in attractive energy with distance so that, for molecules or 

 condensed regions presenting sufficiently large interacting surfaces, 



