Probabilistic aspects of the structure of the collagen fibril

The purpose of this paper is to improve the explanation, given by Woodhead-Galloway & Machin [Acta Cryst. (1976), A32, 368-372] for the marked diffuse near-equatorial X-ray scattering seen in the diffraction patterns of rat-tail tendon and other collagens. That paper suggested a lateral liquid-like disorder among the molecules, but the treatment involved a number of simplifications, the most important being its restriction to an equatorial projection. This paper elaborates on the treatment and provides two different versions each dealing with the problem in three dimensions. The first approach derives the crystallographic consequences of the random-stagger model for the fibril proposed by Grant, Cox & Horne [Nature (London), (1965). 207, 822- 8261. The second approach relaxes the strict crystallography assumed in the treatment of the model of Grant et al. (1965); instead it suggests a stochastic analogy with the theory of Woodhead-Galloway [Acta Cryst. (1977). B33, 1212-1218] for the off-equatorial reflections seen in the diffraction pattern of rat-tail tendon.An addition, the opportunity is taken to remove a discrepancy between theory and experimental results by introducing the fanning of the diffraction pattern (which has its origins in molecular tilting or in fibril shearing).