Helices

Any conformation in which the torsion angles form a repeating pattern, as they are read from one end of the structure to the other.

• Planar zig-zag of crystalline polyethylene. The repeating pattern is trans (there is a trans state at every bond). The structure has two methylene groups per "turn", or per repeat.

• The 3₁ helix of isotactic polypropylene, with three propylene units per turn. The repeating pattern for the torsion angles is trans, gauche.

• The alpha helix of poly(amino acids) such as polyalanine. This structure was described near 50 years ago, Pauling, L.; Corey, R. "Atomic Coordinates and Structure Factors for Two Helical Configurations of Polypeptide Chains"Proc. Natl. Acad. Sci. USA, 1951, 37, 235-240.
  • Poly(L-alanine) forms a right-handed alpha helix, and poly(D-alanine) forms a left-handed alpha helix, the two being mirror images.
  • The torsion angles are 180^o at the amide bond, -48^o at the C-N bond, and -57^o at the C-C bond.
  • The helix has 3.6 amino acid residues per turn.
  • The translation per residue along the helix axis is 0.15 nm
  • The pitch is 0.54 nm. It is the product of the number of residues per turn and translation per residue.
  • The side chains are oriented outward from the helix axis.
  • The C=O and N-H bonds of the backbone are in the core of the helix, and oriented parallel with the helix axis.
  • The helix contains intramolecular hydrogen bonds between amino acid residues i and i+4. There are 13 atoms in the loop closed by the hydrogen bond. Therefore this helix is also called the 3.6₁₃ helix, using the format residues per turn_{atoms in hydrogen-bonded loop}.
  • Many poly(L-amino acids) form right-handed alpha helices under appropriate conditions. In addition to poly(L-alanine), the list includes poly(L-glutamic acid), poly(L-lysine), and poly(L-tyrosine). But neither polyglycine nor poly(L-proline) form an alpha helix.

• The 3.0₁₀ helix of poly(amino acids) such as poly(alpha-aminoisobutyric acid).
  • The helix is wound slightly tighter than the alpha helix (3.6₁₃ helix), and the hydrogen bond has been shifted by one amino acid residue.
  • The torsion angles are 180^o at the amide bond, -60^o at the C-N bond, and -30^o at the C-C bond, which are not too different from those seen in the alpha helix.
  • The translation per residue along the helix axis is 0.20 nm
  • The pitch is 0.60 nm.
  • The side chains are oriented outward from the helix axis.
  • The C=O and N-H bonds of the backbone are in the core of the helix, and oriented parallel with the helix axis.

• The polyglycine Form II helix.
  • No intramolecular hydrogen bonds are possible, because the C=O and N-H bonds are oriented perpendicular to the helix axis.
  • Interchain hydrogen bonds are formed in the crystal.
  • An isolated polyglycine chain does not discriminate between right- and left-handed helices, but there is coordination in the handedness of the helices in a multichain crystal.
  • 3 residues per turn, a translation per residue of 0.30 nm, and a pitch of 0.90 nm.

• The polyproline Form II helix.
  • No intramolecular hydrogen bonds are possible, because there is no hydrogen bond donor.
  • The helix is stabilized by
    • The pyrrolidine ring, which locks the C^alpha-N bond into the torsion angle required for this helix.
    • Repulsive steric interactions between the pyrrolidine rings on successive prolyl residues, which effectively confine the torsion at the C^alpha-C bond to the value required for this helix.
  • Poly(L-proline) prefers the left-handed helix.
  • The backbone conformation is the same as the polyglycine Form II helix: 3 residues per turn, a translation per residuie of 0.30 nm, and a pitch of 0.90 nm.

• The beta sheet of polyalanine, Pauling, L.; Corey, R. B.; Branson, H. R. "The Structure of Proteins: Two Hydrogen Bonded Helical Conformations of the Polypeptide Chain" Proc. Natl. Acad. Sci. USA 1951, 37, 205-211.
  • No intramolecular hydrogen bonds are possible, because the C=O and N-H bonds are oriented perpendicular to the helix axis.
  • Hydrogen bonds are formed between neighboring parallel (or antiparallel) chains in the crystal.
  • 2 residues per turn, translation of 0.345 nm per residue (the chain is almost fully extended), and a pitch of 0.69 nm.
  • Neighboring chains are antiparallel in most beta sheets, but they can sometimes be parallel.
  • The side chains are oriented perpendicular to the axis of the chains, and perpendicular to the direction of the hyrogen bonds.
  • Polyglycine can also crystallize as a beta sheet. That crystal is called polyglycine Form I, to distinguish it from the Form II helix described above.
  • Many poly(L-amino acids) form beta sheets under appropriate conditions. In addition to poly(L-alanine) and polyglycine, the list includes poly(L-glutamic acid), poly(L-lysine), poly(L-tyrosine). But poly(L-proline) cannot form a beta sheet.

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