Peptide Torsion Angles and Secondary Structure

Peptide Torsion Angles

The figure below shows the three main chain torsion angles of a polypeptide. These are phi, psi and omega.

The planarity of the peptide bond restricts omega to 180 degrees in very nearly all of the main chain peptide bonds. In rare cases omega = 0 degrees for a cis peptide bond which, as stated above, usually involves proline.

Development of a Model for Alpha-Helix Structure.

Pauling and Corey twisted models of polypeptides around to find ways of getting the backbone into regular conformations which would agree with alpha-keratin fibre diffraction data. The most simple and elegant arrangement is a right-handed spiral conformation known as the 'alpha-helix'.

The figure below shows how a right-handed helix differs from a left-handed one. An easy way to remember this is to hold both your hands in front of you with your thumbs pointing up and your fingers curled towards you. For each hand the thumbs indicate the direction of translation and the fingers indicate the direction of rotation.

Properties of the alpha-helix.

1. The structure repeats itself every 5.4 Angstroms along the helix axis, ie we say that the alpha-helix has a pitch of 5.4 Angstroms. Alpha-helices have 3.6 amino acid residues per turn, ie a helix 36 amino acids long would form 10 turns. The separation of residues along the helix axis is 5.4/3.6 or 1.5 Angstroms, ie the alpha-helix has a rise per residue of 1.5 Angstroms.

2. Every mainchain C=O and N-H group is hydrogen-bonded to a peptide bond 4 residues away (ie O(i) to N(i+4)). This gives a very regular, stable arrangement.

3. The peptide planes are roughly parallel with the helix axis and the dipoles within the helix are aligned, ie all C=O groups point in the same direction and all N-H groups point the other way. Side chains point outward from helix axis and are generally oriented towards its amino-terminal end.

   

4. All the amino acids have negative phi and psi angles, typical values being -60 degrees and -50 degrees, respectively.

Distortions of alpha-helices.

The majority of alpha-helices in globular proteins are curved or distorted somewhat compared with the standard Pauling-Corey model. These distortions arise from several factors including:

1. The packing of buried helices against other secondary structure elements in the core of the protein.

2. Proline residues induce distortions of around 20 degrees in the direction of the helix axis. This is because proline cannot form a regular alpha-helix due to steric hindrance arising from its cyclic side chain which also blocks the main chain N atom and chemically prevents it forming a hydrogen bond. Janet Thornton has shown that proline causes two H-bonds in the helix to be broken since the NH group of the following residue is also prevented from forming a good hydrogen bond. Helices containing proline are usually long perhaps because shorter helices would be destabilised by the presence of a proline residue too much. Proline occurs more commonly in extended regions of polypeptide.

3. Solvent. Exposed helices are often bent away from the solvent region. This is because the exposed C=O groups tend to point towards solvent to maximise their H-bonding capacity, ie tend to form H-bonds to solvent as well as N-H groups. This gives rise to a bend in the helix axis.

   

4. 3(10)-Helices. Strictly, these form a distinct class of helix but they are always short and frequently occur at the termini of regular alpha-helices. The name 3(10) arises because there are three residues per turn and ten atoms enclosed in a ring formed by each hydrogen bond (note the hydrogen atom is included in this count). There are main chain hydrogen bonds between residues separated by three residues along the chain (ie O(i) to N(i+3)). In this nomenclature the Pauling-Corey alpha-helix is a 3.6(13)-helix. The dipoles of the 3(10)-helix are not so well aligned as in the alpha-helix, ie it is a less stable structure and side chain packing is less favourable.

   

The Beta-Sheet.

Pauling and Corey derived a model for the conformation of fibrous proteins known as beta-keratins. In this conformation the polypeptide does not form a coil. Instead, it zig-zags in a more extended conformation than the alpha-helix. Amino acid residues in the beta-conformation have negative phi angles and the psi angles are positive. Typical values are phi = -140 degrees and psi = 130 degrees. In contrast, alpha-helical residues have both phi and psi negative. A section of polypeptide with residues in the beta-conformation is refered to as a beta-strand and these strands can associate by main chain hydrogen bonding interactions to form a beta sheet.

In a beta-sheet two or more polypeptide chains run alongside each other and are linked in a regular manner by hydrogen bonds between the main chain C=O and N-H groups. Therefore all hydrogen bonds in a beta-sheet are between different segments of polypeptide. This contrasts with the alpha-helix where all hydrogen bonds involve the same element of secondary structure. The R-groups (side chains) of neighbouring residues in a beta-strand point in opposite directions.

Imagining two strands parallel to this, one above the plane of the screen and one behind, it is possible to grasp how the pleated appearance of the beta-sheet arises. Note that peptide groups of adjacent residues point in opposite directions whereas with alpha-helices the peptide bonds all point one way.

The axial distance between adjacent residues is 3.5 Angstroms. There are two residues per repeat unit which gives the beta-strand a 7 Angstrom pitch. This compares with the alpha-helix where the axial distance between adjacent residues is only 1.5 Angstroms. Clearly, polypeptides in the beta-conformation are far more extended than those in the alpha-helical conformation.

Parallel, Antiparallel and Mixed Beta-Sheets.

In parallel beta-sheets the strands all run in one direction, whereas in antiparallel sheets they all run in opposite directions. In mixed sheets some strands are parallel and others are antiparallel.

Below is a diagram of a three-stranded antiparallel beta-sheet. It emphasises the highly regular pattern of hydrogen bonds between the main chain NH and CO groups of the constituent strands.

In the classical Pauling-Corey models the parallel beta-sheet has somewhat more distorted and consequently weaker hydrogen bonds between the strands.

Beta-sheets are very common in globular proteins and most contain less than six strands. The width of a six-stranded beta-sheet is approximately 25 Angstroms. No preference for parallel or antiparallel beta-sheets is observed, but parallel sheets with less than four strands are rare, perhaps reflecting their lower stability. Sheets tend to be either all parallel or all antiparallel, but mixed sheets do occur.

The Pauling-Corey model of the beta-sheet is planar. However, most beta-sheets found in globular protein X-ray structures are twisted. This twist is left-handed as shown below. The overall twisting of the sheet results from a relative rotation of each residue in the strands by 30 degrees per amino acid in a right-handed sense.

Parallel sheets are less twisted than antiparallel and are always buried. In contrast, antiparallel sheets can withstand greater distortions (twisting and beta-bulges) and greater exposure to solvent. This implies that antiparallel sheets are more stable than parallel ones which is consistent both with the hydrogen bond geometry and the fact that small parallel sheets rarely occur (see above).