Abstract

Ramachandran (φ, ψ) maps have previously been used to depict regular, accessible conformations for amylose and other polysaccharides. Because monomeric bond lengths and valence angles are known to be fixed within narrow limits, generation of helical conformations by rotations (φ, ψ) of successive rigid monomers about the two bonds to the linkage oxygen atom was considered to be sufficient. By the Ramachandran method, given values of φ and ψ, combined with a set of residue atomic coordinates and fixed glycosidic angle, result in a helix that can be described in terms of n (number of residues per turn) and h (rise per residue). As we have previously discussed, however, large torsion angle differences within the ring exist for residues from different sources. These differences give rise to differing helical parameters for given values of φ and ψ The Ramachandran map is thus unable to provide a comprehensive picture of the allowed helical conformations. To remedy this difficulty, we have systematically examined combinations of varying values of n and h for feasibility. At each n-h grid point, virtual bond models were examined for reasonable stereochemistry by hard-sphere criteria. If any of the interatomic distances were less than the fully allowed values but greater than the minimally allowed figure, a given model was considered feasible as long as no more than five such marginal contacts occurred per glucose unit. Other than a 2.56 A minimum figure for interoxygen distances, no special allowance was made for hydrogen bonding. The other, slightly smaller, minimally allowed values in the present work were considered reasonable because no attempt was made to optimize the model in order to relieve such short contacts. By examining 13 known residue geometries (all still in the 4C1 conformation but with O(4)-O(1) length from 4.01 to 4.61 A) and allowing models with glucosidic angles between 113°and 122°, a much wider range of helical shapes is found to be feasible than was previously reported. Values of n range from 2 to 10 and h ranges from 0.8 to 4.4 A. The left-handed domain of the n-h map (negative values of n) includes all known amylose conformations, whereas several known extended shapes are not found within the right-handed domain. In both right- and left-handed domains, there is a large central region in which there are no known crystalline forms. Although these forms are likely to be important in amylose solutions, they are less likely to crystallize because of inefficient packing. These helices with moderate h cannot form inter-turn hydrogen bonds nor can they form double helices or “nested” single helices.

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