Flexibility of polyunsaturated fatty acid chains and peptide backbones: A comparative ab initio study

The conformational properties of omega-3 type of polyunsaturated fatty acid (PUFA) chains and their fragments were studied using Hartree-Fock (RHF/3-21G) and DFT (B3LYP/6-31G(d)) methods. Comparisons between a unit (U) fragment of the PUFA chain and a mono N-Ac-glycine-NHMe residue show that both structures C, Zn have the same sequence of sp(2)-sp(3)-sp(2) atoms. The flexibility of PUFA originates in the internal rotation about the above pairs of sigma bonds. Therefore, potential energy surfaces (PESs) were generated by a scan around the terminal dihedral angles (phi(t1) and phi(t2)) as well as the phi(1) and Psi(1) dihedrals of both 1U congeners (Me-CHCH-CH2-CHCHMe and MeCONH-CH2-CONHMe) at the RHF/3-21G level of theory. An interesting similarity was found in the flexibility between the cis allylic structure and the trans peptide models. A flat landscape can be seen in the cis 1U (hepta-2,5-diene) surface, implying that several conformations are expected to be found in this (PES). An exhaustive search carried out on the 1U and 2U models revealed that straight chain structures such as trans and cis beta (phi(1) approximate to Psi(1) approximate to 120degrees; phi(2) approximate to Psi(2) approximate to -120degrees) or trans and cis extended (phi(1) approximate to Psi(1) approximate to phi(2) approximate to Psi(2) approximate to 120degrees) can be formed at the lowest energy of both isomers. However, forming helical structures, such as trans helix (phi(1) approximate to -120degrees, Psi(1) approximate to 12degrees; phi(2) approximate to -120degrees, Psi(2) approximate to 12degrees) or cis helix (phi(1) approximate to 130degrees, Psi(1) approximate to 90degrees; phi(2) approximate to 145degrees, Psi(2) approximate to 90degrees) will require more energy. These six conformations, found Z, in 2U, were selected to construct longer chains such as 3U, 4U, 5U, and 6U to obtain the thermochemistry of secondary structures. The variation in the extension or compression of the chain length turned out to be a factor of 2 between the helical and nonhelical structures. The inside diameter of the tube of cis helix turned out to be 3.5 Angstrom after discounting the internal H atoms. Thermodynamic functions were computed at the B3LYP/6-311+G(2d, p)//B3LYP/6-31(d). The cis-trans isomerization energy of 1.7 +/- 0.2 kcal mol(-1) unit(-1) for all structure pairs indicates that the conformer selection was consistent. A folding, energy of 0.5 +/- 0.1 kcal mol(-1) unit-(1) has been extracted from the energy comparison of the helices and most extended nonhelical structures. The entropy change associated with the folding (DeltaS(folding)) is decreases faster with the degree of polymerization (n) for the cis than for the trans isomer. As a consequence. the linear relationships between (DeltaG(folding)) and n for the cis and trans isomer crossed at about n = 3. This suggested that the naturally occurring cis isomer less ready to fold than the trans isomer since a greater degree of organization is exhibited by the cis isomer during the folding process. The result of this work leads to the question within the group additivity rule: could the method applied in our study of the folding of polyallylic hydrocarbons be useful in investigating L the thermochemistry of protein folding?