Section 19.5.1. Introduction

Many biopolymers are long helical structures and have a natural tendency to form fibres. This tendency severely impedes the growth of single crystals from these polymers, and even if crystals can be grown, the molecular interactions in the crystals rarely correspond to the biologically significant interactions in the fibres. Conventional macromolecular crystallography is therefore often not applicable to these systems. Fibre diffraction, however, is a powerful technique for determining the structural details of such polymers. It has been used to study a wide variety of biopolymers, ranging from simple polypeptides, polynucleotides and polysaccharides to complex filamentous viruses and cytoskeletal filaments.

Fibres can have relatively high degrees of order, although falling short of true three-dimensional crystallinity. The key difference between fibres and crystals, however, is that in fibres the fundamental structural aggregates, although parallel to each other, are randomly oriented about the fibre axis. Consequently, the diffraction pattern is cylindrically averaged. This cylindrical averaging is the defining characteristic of fibre diffraction.

On the basis of this definition, fibre diffraction may also be considered to include diffraction from many biological membrane specimens, and much of fibre-diffraction theory also applies to membrane diffraction. In general, however, the diffracting units in fibres have helical symmetry, whereas those of membranes do not.

In addition to the loss of information due to cylindrical averaging, fibre-diffraction patterns reflect a generally limited degree of order and rarely extend beyond 3 Å resolution. Consequently, the number of data obtainable from a fibre is considerably less than that from a single crystal having a similar size of asymmetric unit. The use of stereochemical information to supplement the diffraction data is therefore essential. For polymers with small asymmetric units, such as polynucleotides, structural chemical information can be used to construct models consistent with the helical parameters and molecular dimensions obtained from the diffraction data. For the larger asymmetric units found in aggregates, such as viruses, initial models must be constructed in other ways. However, in all cases the combination of diffraction data and stereochemistry can be used to refine both molecular structures and packing parameters. Refinement in this way is very similar to that used in macromolecular crystallography, but because of the limited number of experimental data, stereochemical restraints are particularly important in fibre diffraction. As in crystallography, difference-electron-density maps are used in conjunction with refinement to identify missing portions and determine the correctness of the models and, in favourable cases, to locate ions and solvent molecules associated with the polymers.