Accurate X-ray diffraction analysis of fibrous polysaccharides containing pyranose rings. Part I. The linked-atom approach

X-Ray diffraction data from polymers are, by themselves, rarely sufficient to allow determination of atomic positions within a few tenths of an Ångstrom. When this accuracy is required, the polymer diffraction data have to be supplemented by stereochemical data from accurate analyses of relevant monomers. The linked-atom least-squares approach is a logical and convenient procedure for achieving the necessary synthesis of different types of data. The procedure has been used extensively in analysing polynucleotides and polypeptides but not, so far, polysaccharides. Its adaptation for these is described, with particular attention being paid to the precise conformations of rings that dominate the geometry of these polymers.Since the determination of accurate structures of polysaccharides depends both on diffraction data from the polymers themselves and on additional data such as bond-lengths and bond-angles, we present a survey of the values of these latter quantities as determined by X-ray diffraction analysis of single crystals of appropriate small molecules.As examples of the application of linked-atom least-squares methods we present and discuss the preparation of standard α- and β-D-glucose rings and preliminary molecular models of chitin and ι-carrageenan.