Correlated variations of bond lengths in pseudorotating furanose rings

Correlated variations of bond lengths in pseudorotating furanose rings are investigated by a theoretical method. At first, matrix equations are proposed to determine the spatial coordinates of the ring atoms from the bond lengths, the bond angles, and the pseudorotation parameters. Secondly, a necessary functional form of the variations of the bond lengths of five-membered rings is derived from a consideration of symmetry. Finally, demonstrations are performed on a furanose ring whose bond angle variations have been precisely determined by experimental analyses. The resulting bond length variations are: delta Ri = beta icos(8/5 pi.(i-2)+2P) where delta Ri is the variation of the bond length between atoms i and i+1, P is the pseudorotation phase, and beta i is a negative constant about -0.01 A. These bond length variations are balanced on the apparent strains of the bond lengths and the bond angles.