The Formation of Natural Membranes 439 



and again. That is the way followed in a growing crystal. Once the periodicity is 

 established there is no definite Hmit to the size of the aggregate. The other way 

 is that of building up a more and more extended aggregate without the dull 

 device of repetition. That is the case of the more and more compUcated organic 

 molecule in which every atom, and every group of atoms, plays an individual 

 role, not entirely equivalent to that of many others (as is the case in a periodic 

 structure). We might quite properly call that an aperiodic crystal or solid and 

 express our hypothesis by saying: 'We believe a gene — or perhaps the whole 

 chromosome fibre — to be an aperiodic crystal'. Generalizations which follow 

 from a knowledge of the structure of proteins, deoxyribonucleic acid, and syn- 

 thetic polymers allow us to add to Schrödinger's two classes of solids an inter- 

 mediate group of semiperiodic solids. These may be described as being formed 

 upon a backbone, sheet, or lattice, of regular periodic structure, attached to 

 which at regular intervals there are groups of atoms that may be different in 

 different parts of the structure. These solids have a most important property 

 which is lacking in the aperiodic group : they may be formed by a simple repe- 

 titive process of poljrmerization of monomeric constituents which would give 

 rise to a random arrangement of the aperiodic part of the structure unless this 

 arrangement were determined by some added spatial constraint. In the semi- 

 periodic soUds formed upon a three-dimensional periodic lattice, there is no 

 obvious molecular mechanism for the apphcation of the constraint required to 

 arrange the aperiodic part, but for the laminar and linear cases the constraint 

 can be due to the juxtaposition of another semiperiodic structure, tending to 

 lower the free energy of the particular aperiodic arrangement by residual bonding 

 with it. Such is the essential molecular basis of all template hypotheses, even 

 though they may invoke the mediation of the surfaces of enzymes to couple the 

 process of potymerization to the placing of the monomers upon the semiperiodic 

 template [9]. The two semiperiodic polymers concerned would be related to 

 each other in the sense that either might cause the orderly polymerization of the 

 other — with only occasional mistakes in arrangement (mutations), the frequency 

 of which would partly depend upon the tightness of coupling between the poly- 

 merization process and the placing of monomers on the complementary semi- 

 periodic solid. The periodic parts of the two solids might be the same or different, 

 and in either case a synthesis of the appropriate polymer would be expected to be 

 driven forward by the supply of the appropriate proportions of its monomers. A 

 deficit of one of the monomers would be expected to lead to slowing of poly- 

 merization and to accumiilation of the other monomers — a condition which could 

 exert a regulatory effect on the flow of the monomers. As pointed out earlier, 

 the replication in this way of semiperiodic solids would be expected to be re- 

 stricted to the linear and laminar groups. Of these, however, the linear group 

 would display the more versatile properties, particularly if free rotation were 

 possible around the bonds of the backbones; for this would allow the long-chain 

 soHd greater freedom of aUgnment with another semiperiodic chain, and it might 

 also close-pack upon itself, possibly in a number of alternative stable configura- 

 tions. 

 Watson & Crick [5] suggested that the replication of the paired complementary 



