Description of irregularity in biological structures

A systematic theoretical analysis is made of the kinds of structural irregularity which occur in biological systems. The theoretical problems investigated were: (1) the precise meaning of the term 'paracrystal' when applied to biological systems such as tropomyosin tactoids, collagen fibrils, keratin and the myelin sheath of nerve; (2) the relationship between the paracrystal and liquid-theory descriptions of disorder which have recently been applied to the structure of collagen fibrils; (3) how structural irregularity affects the diffraction patterns (X-ray, neutron and electron) which are commonly used to investigate the structure of these systems experimentally. The conclusions are: (I) paracrystalline disorder of the first kind refers to a spatially disordered crystal but for biological systems it would generally be impracticable to distinguish this from thermal disorder; (2) paracrystalline disorder of the second kind provides a conceptually clumsy method for describing liquid-like systems; (3) paracrystal models are not strictly valid for finite systems; (4) modern liquid theory, as applied, for example, to the structure of the collagen fibrils, provides an elegant and economical alternative to paracrystal theory for disorder of the second kind; (5) the presence of peaks in diffraction patterns from biological systems does not necessarily imply that the system has very much regularity, i.e. it is not evidence for the existence of a lattice.