The Scale of Structural Units in Biopoesis 



389 



particles with respect to a third particle in its vicinity. In (a) in the region of 

 the potential minimum there is a shallow trough along the axis of the particle 

 pair, in (c) it Hes along the equator. The addition of a third particle to the system 

 will be coUinear in the case of (a) and triangular in that of (c) (Fig. 3 b and d). 

 It is easy to see that this will lead, with further additions, to the formation of a 

 fibre in the first case and a close-packed crystal in the other without there being 

 much to choose between them in their mutual energies of association. This is 

 borned out in practice by the very common occurrence of the so-called reversible 

 fibrous-globular (f-g) transition in many proteins of which that of insuHn has 

 been most studied [4]. The fibrous association may be, so to speak, vulcanized 

 by primary valence formation as in the case of the physiologically important 

 fibrinogen-fibrin transformation, so as to make reversibility difficult. 



(b) ^-^ -^ (d) 



Fig. 3. Determination of type of co-ordination of particles in two dimensions 

 by shape of mutual equipotential curves. 



(a) and (b) — with troughs of potential along axis leading to linear co-ordination i 

 (c) and (d) — with troughs of potential at right angles to axis leading to close-packed 

 agglomerations. O — potential minima; -> — direction of attachment of further 



particles. 



A co-ordination number of one can only lead to a particle pair, but such pairs 

 seem to be common among the proteins, notably in insuHn where the chemical 

 unit of 5500 molecular weight is nearly always found in solution as 11,000 or 

 some higher multiple, 33,000 or 44,000. It also arises when a single metal atom 

 is co-ordinated with protein molecules, as in the case of the mercury-albumin 

 complexes. Here steric co-ordinations limit the association to two, which will 

 be the general rule where the co-ordinating agent is small compared to the co- 

 ordinated [30]. 



