The thesis is focused on the studies of β-peptide systems by using theoretical ab initio quantum mechanical computational approach. β-Peptides form various secondary structures such as 14-helix, 12-helix, 10/12-helix, and pleated-sheet structures depending upon substitution pattern. It is useful to understand the intrinsic stabilities and the substituent effects of the stabilities of secondary structures of β-peptides. _{n 2}...[ Read more ]

The thesis is focused on the studies of β-peptide systems by using theoretical ab initio quantum mechanical computational approach. β-Peptides form various secondary structures such as 14-helix, 12-helix, 10/12-helix, and pleated-sheet structures depending upon substitution pattern. It is useful to understand the intrinsic stabilities and the substituent effects of the stabilities of secondary structures of β-peptides.

Chapter 2 focuses on the intrinsic stabilities of the secondary structures. We have studied theoretically a series of poly-β-alanine models, Ac-(β-A1a)_n-NH₂, with up to n=9 residues. Interactions among residues, which results in cooperativity, is discussed based on calculated residue energies. While no cooperativity is found for the formation of the β-strand, C6-ribbon and 2₈-ribbon, which have constant residue energies, there is a considerable positive cooperativity for the formation of the 10-helix, 12-helix and 14-helix, which have increased residue energies as peptide elongates. The residue energy of the 10/12-helix increases significantly for n=2 and 3, and then displays a zigzag pattern as peptide elongates. There is a good correlation between calculated residue energies and residue dipole moments, indicating the importance of long-range electrostatic interaction to the cooperativity.

In Chapter 3, the substituent effects have been evaluated with a pentapeptide model. Geometries were optimized with a repeating unit approach for four types of mono-methyl substitutions. The favored secondary structures of peptides formed by mono-methyl substituted amino acids can be derived. Di- and tri-substitutions can also be evaluated based on these calculations. We predict that like-β^2,2,3-peptides prefers the C₆-ribbon structure, while the unlike-β^2,2,3-peptides prefers the alternate C₆-ribbon structure. Studies on β-sheet are isolated in chapter 4. The calculated intrinsic hydrogen bond strength is large for both parallel and antiparallel β-sheets and affected little by substituents when they are perpendicular to the backbone. The unlike-β^2,3-peptides are the best for β-sheet-formation because their backbones prefer extended conformation, which is ideal for β-strand conformation. β-Sheets are predicted to adopt twisted geometries. There is a large cooperativity for the formation of hydrogen bond network in β-sheets in the perpendicular direction due to long-range electrostatic attractions since all carbonyl groups are roughly in the same direction.

In Chapter 5, we have studied six α-hydroxyl-β-amine acid models. A 7-m-r hydrogen-bonded conformation is found to be most stable for Models 15, 16, and 17. This conformation is in equilibrium with other low energy conformations. In the case of model 18, a 7-m-r conformation with a terminal acid adopting (Z) form was found to be more stable due to the favorable electrostatic interaction between the α-hydroxyl group and the acid hydroxyl group. This conformation disappears for model 19, where the acid group is replaced with an ester group. For model 19, two conformers are quite similar in stabilities. The model 20 is predicted to exist in an extended conformation, which is very similar to that of Kni-272, an anti-HIV protease inhibitor in the enzyme bound state.