MOLECULES AND STRUCTURE FORMATION 11 



homogeneous. Aggregations of the fibrils themselves may lead to 

 the formation of spherites. 



It is clear that, at least over a portion of its development, the 

 fibril axial ratio increases with fibril mass. That an asymmetric 

 aggregate should form when charged molecules link, without speci- 

 fication of surface structure, has been pointed out by Rees ( 1951 ) . 

 This is because the electrostatic-potential barrier is lowest at the 

 ends of the dimer or other asvmmetric unit. However, the coopera- 

 tive effect itself will exert a strong directional influence. This is 

 illustrated in Fig. 1, which is a possible arrangement for the insulin- 

 fibril nucleus. The stable structure is formed when any fourth 

 insulin unit is added to the correct previous group of three. There- 

 after, insulins are expected to add most frequently in a manner 

 which perpetuates this stable structure; consequently, the aggregate 

 elongates in the direction of the cylinder axis of Fig. 1. 



Stable Colloids. The interactions of the caseins (Waugh, 1958) 

 reveal both specificity of interaction and cooperative effects, the end 

 result in milk being a population of micelles varying in chemical 

 composition and volume, the latter over a range of about 350 fold. 

 Yet the micelles are in rapid equilibrium with their constituent 

 components in solution, some of which are relatively insoluble under 

 the conditions where micelles readily form. The most important 

 initial interaction in micelle formation occurs between a^- and 

 k-caseins, and in this interaction secondary valence and charge in- 

 teractions arrive at a remarkable mutual satisfaction. Here, a^-casein 

 is a phospho-protein of M ~ 23,000. It has a phosphorus content of 

 over 1 per cent but no disulfide. Physically, this protein appears to 

 be a single coil 210 A in length and 16 A in diameter. In the absence 

 of calcium the protein is a highly soluble polymer; the polymer be- 

 comes quite insoluble in the presence of calcium. The k-casein is 

 also apparently a single coil about 150 A long, which contains disul- 

 fide but little phosphorus. It forms soluble, condition-insensitive 

 polymers of 13.5 S in the presence or absence of calcium. When mix- 

 tures are made containing molecular ratios of 3 a^-casein to 1 

 k-casein, the original polymers disappear and a stoichiometric a,- 

 k-casein complex forms. This complex can form in the absence of 

 calcium and under conditions where both of the monomers carry a 

 high 'net negative charge. One must assume that here, as in other 

 cases, secondary valence forces are responsible for association. In 

 this connection, an examination of the amino acid compositions of 



