Theoretical studies of peptides : secondary structures of [alpha]-peptides & [gamma]-peptides

This dissertation focuses on the theoretical studies of secondary structures of α-peptides (Chapters 2-5) and γ-peptides (Chapters 6 and7) by using quantum mechanics and molecular mechanics computation methods. Chapter 1 is an introduction on the background and current understanding of secondary structures of proteins. Chapter 2 presents a computational study using a repeating unit approach to delineate the preferences of β-strand, 27-ribbon, 310-helix, and α-helix as a function of peptide sequence length. There is significant cooperativity in the formation of 310- and α-helices, especially for the α-helix, whereas there is no cooperativity in the formation of β-strands and 27-ribbons. A good correlation between residue energy and residue dipole moment was uncovered, indicating the importance of long-range electrostatic interactions to the cooperativity. Chapter 3 presents a theoretical study on a series of β-sheet models. The results indicate that antiparallel and parallel β-sheets have the same pattern of cooperativity. No cooperativity is found along the parallel direction. In the perpendicular direction, cooperativity attenuates with elongation of strands. Our study suggests that hydrogen bond is mainly due to electrostatic interaction. The study of the binding energies of parallel and antiparallel β-sheets as functions of backbone pleating is presented in Chapter 4. It has been found that the parallel β- sheet intrinsically favors to be pleated with backbone dihedral angle -φ and ψ of about 120-130°, while the antiparallel β-sheet has a strong intrinsic binding energy in a large range of backbone dihedral angles (-φ and ψ of 120-180°). Since backbone pleating is necessary for residues with large side-chains, the results allow us to address a series issues about β-sheet formation including structural features, parallel/anti-parallel preference, β-sheet-forming propensities, and residue paring of β-sheets. Chapter 5 gives a detailed analysis on the difference in binding energy between the large hydrogen-bonding ring and small hydrogen-bonding ring in the antiparallel β-sheet. It is found that multiple-body electrostatic interactions involving Cα-H and amide carbonyl groups (instead of simple Cα-H---O=C hydrogen bonds) contribute importantly to the stability of β-sheets. In Chapter 6, a conformational search for the helical structures of γ-peptides is presented. It has been found that a nine-membered-ring hydrogen-bonded structure is most stable for a dipeptide model. For peptides with more than 4 γ-amino acid residues, a 14-helical structure becomes more stable. In Chapter 7, a repeating uniting approach is applied for the study of cooperativity in 9-, 12-, 14-helices of γ- peptides. It has been found that there is no cooperativity in the 9-helix but there is cooperativity in the formation of the 12- and 14-helices. The detailed electrostatic and steric interactions in the three types of helices have also been derived