Long-range effects in oligopeptides. A theoretical study of the β-sheet structure of Gly_n (n = 2-10)

Long-range interactions in the β-sheet structure of oligoglycines Gly_n (n = 2-10) have been investigated by DFT computations using the B3LYP exchange-correlation functional in conjunction with a diffuse polarized valence triple-ζ basis set. The study focused on the evaluation of the title interactions in the Gly_n chain and on the quantitative determination of their consequences in both energy and geometry. It was found that the interactions contribute considerably to the stability of the β-sheet and have a substantial impact on the geometrical parameters. On the basis of the gradual build-up of energetic and geometrical effects, we determined the effective radius of long-range interactions to be around 10 Gly units in the β-sheet Gly_n. The energy gain from the long-range interactions of a Gly unit is around 2.5 kJ/mol, stemming to a large extent from the strengthening of the N-H⋯O=C hydrogen bonds. Among the geometrical parameters, the H⋯O hydrogenbond length is the most sensitive to long-range effects, decreasing by several hundredths of an angstrom. Besides, there is a pronounced shortening of the C-N bonds (up to 0.009 Å), while the other bond distances vary within 0.002 Å and the bond angles within 0.5°. Our structure analysis revealed also a small (a few thousands of an angstrom) elongation versus contraction of the chain depending on the parallel versus antiparallel orientation of the NH₂ and COOH end-dipoles. The alterations of the bond distances upon long-range effects are associated with appreciable changes in the magnitude of the main hyperconjugation interactions.