Helical signature motif in the fibre diffraction patterns of random-walk chains

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Helical geometry is one of the most dominant structural features in polypeptides, nucleic acids, carbohydrates and long-chain polymers in general. Structures of a large number of helical biomolecules and important non-biological polymers have been determined by fibre diffraction and helical diffraction theory. This paper reports on a study of fibre diffraction patterns calculated for two different on-lattice random-walk models of polymers, with no built-in helical features. It is noted that such on-lattice random walks are natural models for polymers with fixed monomer geometries and inter-monomer angles. The presence of layer-line intensities is observed, characteristic of fibre diffraction patterns from helices with an integral number of units per turn. It is shown that under certain circumstances, fibre diffraction patterns of helical objects may be difficult to distinguish from cylindrically-averaged fibre diffraction patterns of random walks on lattices with fixed angles. A simple correspondence is demonstrated between the parameters of a helix and a random-walk chain with equivalent fibre diffraction patterns. These results call for a critical examination of the way the helical diffraction theory is typically used: certain structures that have been modelled as helical might, under some circumstances, be more naturally described as random-walk chains with no preferred conformation even on the shortest length-scale and in the context of a fibre.