ABSTRACT: The bihelical (figure of "infinity") topology was examined from vantages of design, crystal structures, chirality, circular dichroism (CD) studies and molecular-orbital calculations. The minimalistic design envisaged the sequential linking of cystine to the anchor diphenic acid, which proved to be a general conformational lock. The bihelical compound 4 was obtained in two steps from diphenic anhydride 1 and cystine di-OMe. The chirality of 4 arises largely from the L-cystine. The bihelical compound 5 obtained from D-cystine di-OMe was found, by X-ray crystallography, CD studies, and optical rotation, to be the perfect mirror image of 4 prepared from L-cystine. The crystal structure of prototype 8, prepared by protocols used for 4 from the achiral cystine analogue cystamine, had a "U"-shaped conformation held together by intramolecular hydrogen bonds. Analysis of 4 and 5 show that the pairs of nine-membered beta-turn-like constructs made compact through hydrogen bonding with DMSO hold the key for the bihelical conformation. Another factor is the need for the presence of a ligand at the Calpha position. The absence of this, as in 8, allows major flexibility in the torsional angles around this critical region, promoting flexible alternatives. The CD analysis of 4, confirmed to be bihelical by X-ray crystallography, showed a typical negative band at about 210 A attributed to the beta-turn-like motif, and in the positive-band region a peak at about 227 A, generally related to the twist of the biphenyl unit. The cystamine analogue 8, which showed a "U"-type structure, presented a CD spectrum with no typical features. The total energy, derived from theoretical calculations by using the X-ray structure data, support the bihelical structure for 4 and a "U"-shaped one for 8. The limited utility of such calculations was tested with composite 9. Composite 9, in which the anchor diphenic acid is linked to cystamine on the one hand and to cystine on the other, showed a CD spectrum similar to that of 4, and this coupled with molecular-orbital calculations, using data from 4 and 8, predict a bihelical structure for this compound.
