34© FINE-STRUCTURE OF PROTOPLASMIC DERIVATIVES III 



thus folded comes to 5.06 A. As the diagram shows (see Fig. 171a), 

 the chain length is doubled at full stretch (100% elongation). 



The ingenious theor)^ of folding to form piperazine rings is con- 

 fronted with steric difficulties ; for the side chains R, which point in 

 the same direction, come so close together that they hinder each other 

 spatially. Astbury and Bell (1941) have therefore drawn up a new 

 folding diagram for the /5-a transformation, which satisfies the 

 following conditions : 



I. The a-form must be about half as long as the ^^-form. 2. The 

 density must remain practically constant. 3. The folds must repeat at 

 a distance of about 5.1 A. 4. The side chains must stand out alternately 

 on one side and the other of the plane of the fold. 5 . The folds must 

 be nowhere so sharp as to have insufficient room for the side chains. 



This diagram is reproduced in Fig. 171b. Side chains pointing 

 upwards are marked R enclosed in a full-line circle and those pointing 

 downwards by R within a dotted circle. The side chains standing on 

 the same side form groups of three, which in the diagram appear as 

 the angles of the triangles indicated. 



The R side chains are particularly important. If hairs stretched in 

 steam at 100° C are dried in the extended state, the elongation loses 

 its reversibility and is retained. The side chains of neighbouring poly- 

 peptide chains enter into spatial relationship and connect the primary 

 valence chains to a kind of grid (Fig. 172). The distance between the 

 bars of the grid is 9.8 A; hence the side chains, which at intervals of 

 3.38 A stand off more or less perpendicularly from the primary chains 

 to the right and left, should have half that length. The thickness of 

 the grid corresponds to the backbone thickness of the stretched, 

 zig-zag polypeptide chains and is therefore 4.5 A. 



Glutamic acid, arginine and cystine are among the most important 

 products of the hydrolysis of wool (see Fig. 88, p. 133). Assuming 

 amidic linking between glutamic acid and arginine, there will be 

 a kind of rung linking two primary valence chains, as represented in 

 Fig. 172 b. Retaining the tetrahedral angle, this side connection would 

 be about 12.5 A long. It is, therefore, of the order of magnitude of 

 the length found by X-ray measurement, viz., 9.8 A, for it is quite 

 conceivable that the chains may somehow be shortened. 



Cystine is the most interesting of the three. This contains two amino 

 acid residues united by a sulphur bridge. It is assumed (Astbury, 



