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Packing analysis of carbohydrates and polysaccharides. IV. A new method for detailed crystal structure refinement of polysaccharides and its application to V‐amylose

A method is described for predicting and solving crystal structures of linear homopolysaccharides. The method is based on the refinement of the structure with respect to either stereochemical constraints or x‐ray diffraction intensities. In the refinement process, all conformational and packing features of the molecule, such as bond lengths, bond angles, conformational angles, nonbonded contacts, hydrogen bonds, etc., can be allowed to vary until the structure reaches both a conformation and crystalline packing that are in minimum disagreement with the stereochemical restraints and the diffraction data. In this fashion, both packing and conformational features of the structure can be simultaneously refined, and not separately as has been the custom in the past. The refinement procedure is based on a method of constrained optimization which possesses improved characteristics of reaching a solution and avoiding false minima, in comparison with least squares methods. The procedure is, in addition, capable of easily finding molecules of solvent of crystallization. The method was applied to further refining the previously solved crystal structure of V‐amylose. The results indicated that contrary to the previously found six‐fold molecular symmetry in the P212121 space group, the V‐amylose molecule exhibits only two‐fold symmetry with the asymmetric unit consisting of three glucose residues in one‐half turn of the helix. The three residues are nonequivalent principally due to unequal rotational positions of the hydroxymethyl groups. The crystal structure of V‐amylose predicted from stereochemical refinement was identical in all details with that obtained from refining against X‐ray data. The excellent agreement with the diffraction data was indicated by the crystallographic disagreement index R = 0.25.