1 Secondary structure and backbone conformation

1.1 Main Chain Torsion Angles

The figure below shows the three main chain torsion angles of a polypeptide. Phi (Φ; C, N, C_α, C) and psi (Ψ; N, C_α, C, N) are on either side of the C_α atom and omega (ω; C_α, C, N, C_α) describes the angle of the peptide bond. While Φ and Ψ have considerable rotational freedom, ω is planar. This is a result of the partial double bond character of the peptide bond which is caused by resonance effects, i.e. delocalized electrons (N-C=O <-> N+=C-O-). A trans configuration (≈180°) is preferred for steric reasons. Cis configuration (≈0°) is rare, except for prolines.

Peptide torsion angles and indication of resonance in the peptide bond — **Peptide torsion angles**. A chain of two amino acids with the three torsion angles phi (Φ), psi (Ψ) and omega (ω). Resonance of peptide bond affecting ω is indicated in light blue.

A "C-N" bond is called amine bond, while "O=C-N" is an amide (with one hydrogen or organic group on the carbon and two on the nitrogen). The peptide bond is neither a pure C-N bond, nor is it a C=N bond. Rather two main canonical structures exist (N-C=O and N+=C-O-) simultaneously.

1.2 The Ramachandran Plot

While the ω angles are restricted, the polypeptide main chain exhibits considerable freedom to rotate around the N-C_α (Φ) and C_α-C (Ψ) bonds. This is visualized in the Ramachandran plot. GN Ramachandran (Ramachandran, Ramakrishnan, and Sasisekharan 1963) used computer models of small polypeptides to systematically sample the Φ/Ψ space with the objective of finding stable conformations. For each conformation, the structure was examined for close contacts between atoms. Atoms were treated as hard spheres with dimensions corresponding to their van der Waals radii (two different sets of VdW parameters were used, including some more flexibility in the backbone in one case). Therefore three parts of the plot were calculated, the fully allowed part (favoured), outer limit (allowed) and disallowed part, where atoms would clash in both cases. Below is the Ramachandran plot based on the orignal [from Wikimedia]

A Redrawn Ramachandran Plot, based on the original. — **Ramachandran plot** from wikimedia based on the original plot by Ramachandran et al. Favoured, or fully allowed region, is marked with solid black lines, allowed, or outer limit region, is represented with a dotted black line.

Ramachandran et al. could assign key secondary structures to specific regions in the plot. In the favoured (or fully allowed part, as they named it) region the beta sheets, the polyproline helix and the (right handed) alpha helix occur. The outer limit, which was calculated with smaller VdW radii brought out an additional region which corresponds to the left-handed alpha-helix.

L-amino acids cannot form extended regions of left-handed helix but occasionally individual residues adopt this conformation. These residues are usually glycine but can also be asparagine or aspartate, where the side chain forms a hydrogen bond with the main chain and therefore stabilises this otherwise unfavourable conformation. The 3₁₀ helix occurs close to the upper right of the alpha-helical region and is on the edge of the allowed region indicating lower stability. Disallowed regions generally involve steric hindrance between the side chain atoms and main chain atoms. Glycine has no side chain and therefore can adopt Φ and Ψ angles in all four quadrants of the Ramachandran plot. Hence it frequently occurs in turn regions of proteins where any other residue would be sterically hindered.

With ever increasing numbers of experimentally determined protein structures, newer iterations of the Ramachandran plot are based on distributions extracted from experimental data. The general case largely corresponds to the original work displayed above. However, glycine and proline exhibit very characteristic properties owed to their sidechains. Glycine has only a single hydrogen as sidechain which leads to less steric hindrance and thus increased rotational freedom around the main chain torsion angles. The sidechain of proline connects with its nitrogen forming a loop. The result is an exceptional conformational rigidity.

General (No Proline or Glycine)
Ψ
	Φ

Glycine Only
Ψ
	Φ

Proline Only
Ψ
	Φ

Pre-Proline Only
Ψ
	Φ

99.7% are within the first contour line
95.0% are within the second contour line
80.0% are within the third contour line

The Ramachandran plots displayed above represent all Φ/Ψ torsion angles extracted from 12,521 non redundant experimental structures (pairwise sequence identity cutoff 30%, X-ray resolution cutoff 2.5Å) as culled from PISCES.

1.3 The alpha-helix.

1.3.1 Development of an alpha-helix structure model.

Pauling and Corey twisted models of polypeptides 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'.

Side-view of an alpha helix. — **Alpha-helix.** Left: Side view of an alpha helix. The N-terminal part of the peptide is to the left. Top left: The molecules are depicted in licorice. Hydrogen bonds are shown with green dotted lines. Bottom left: same view in VdW style. Right: View into an alpha-helix. The N-terminal part is in front. For clarity only the backbone and C_β carbon of the protein is shown.

Top view of an alpha helix. — **Alpha-helix.** Left: Side view of an alpha helix. The N-terminal part of the peptide is to the left. Top left: The molecules are depicted in licorice. Hydrogen bonds are shown with green dotted lines. Bottom left: same view in VdW style. Right: View into an alpha-helix. The N-terminal part is in front. For clarity only the backbone and C_β carbon of the protein is shown.

**Example of a protein with an alpha helix content of >80%** Left: Cartoon view of human adenosine A1 receptor A1AR-bRIL, pdb entry: 5UEN. Right: Ramachandran plot for all non-proline/glycine residues.

Ramachandran plot of human adenosine A1 receptor A1AR-bRIL, pdb entry: 5UEN — **Example of a protein with an alpha helix content of >80%** Left: Cartoon view of human adenosine A1 receptor A1AR-bRIL, pdb entry: 5UEN. Right: Ramachandran plot for all non-proline/glycine residues.

1.3.2 Properties of the alpha-helix.

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

Every main chain C=O and N-H group is hydrogen-bonded to a peptide bond 4 residues away (i.e. O_i to N_i+4). This gives a very regular, stable arrangement.
The peptide planes are roughly parallel with the helix axis and the dipoles within the helix are aligned, i.e. 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.
Φ and Ψ are both negative.

An easy way to remember how a right-handed helix differs from a left-handed one 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.

1.3.3 Distortions of alpha-helices.

The majority of alpha-helices in globular proteins are curved or distorted somewhat compared with the idealized alpha-helix model proposed by Pauling and Corey. These distortions are not linked to violated dihedral angles according to Ramachandran and arise from several factors including:

The packing of buried helices against other secondary structure elements in the core of the protein.
Proline residues induce distortions of around 20° in the direction of the helix axis. This is because Proline cannot form a regular α-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. 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 (read more). Helices containing Proline are usually long perhaps because shorter helices would be destabilized by the presence of a Proline residue too much. Proline occurs more commonly in extended regions of polypeptide.
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 maximize their H-bonding capacity, i.e. tend to form H-bonds to solvent as well as N-H groups. This gives rise to a bend in the helix axis.

1.4 3₁₀-Helices.

3₁₀-Helices form a distinct class of helix but they are generally short and frequently occur at the termini of regular alpha-helices. The name 3₁₀ 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 (i.e. O_i to N_i+3). In this nomenclature the Pauling-Corey alpha-helix is a 3.6₁₃-helix. The dipoles of the 3₁₀-helix are not so well aligned as in the alpha-helix, therefore it is a less stable structure and side chain packing is less favourable.

Side and top view of a 3(10) helix — **A small stretch of a 3₁₀-helix**. The helix is shown in licorice style. Only the backbone and C_β atom is shown for clarity. Left: side view, The 10 atoms of the three amino acids are numbered and the hydrogen bond is indicated as a green dotted line. Right: top view (N-terminal above the clipping plane).

1.5 The beta-sheet.

1.5.1 The beta-sheet structure.

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 Φ angles and the Ψ angles are positive. Typical values are Φ = -140 degrees and Ψ = 130 degrees. In contrast, alpha-helical residues have both negative Φ and Ψ angles. A section of polypeptide with residues in the beta-conformation is referred to as a beta-strand and these strands can associate by main chain hydrogen bonding interactions to form a 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.

Beta-sheets are often depicted as arrows. Conventionally the arrow points towards the C-terminal part of the peptide.

Single strand of a beta-sheet — **View of a single beta-strand**. The dark green box marks the plain of the beta sheet. On top the plain is in line with the monitor. The bottom strand is rotated 90º and the plain is sticking out of the monitor.

Imagine two strands parallel to the ones shown above, either in the plane with the strand (top strand), or one in front of the screen-plane and one behind (bottom strand). This is 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 Å. There are two residues per repeat unit which gives the beta-strand a 7 Å pitch. This compares with the alpha-helix where the axial distance between adjacent residues is only 1.5 Å. Clearly, polypeptides in the beta-conformation are far more extended than those in the alpha-helical conformation.

1.5.2 Parallel, antiparallel and mixed beta-sheets.

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

Abstract representation of different beta sheets and snippets of real proteins representing it. — **Different types of beta sheets**. Hydrogen bonds are represented with dotted lines. Both a schematic representation and snippets from protein structures are shown. For clarity only the backbone heavy atoms and C_β atoms, where applicable, are shown. (Anti parallel sheet is a snipped from PDB code 5KO0, parallel from 1DAB and mixed from 4TVW)

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 Å. 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.

Schematic and real example of the left handed twist found in many beta-sheets. — **View into a beta-sheet**. Note the rotation between the strands. Schematic view (top) and part of a beta sheet (pdb entry: 4TVW). For clarity only the backbone heavy atom and C_β is shown.

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).

1.6 Coils and turns

1.6.1 beta-turns (reverse turns)

A beta turn is a region of four consecutive residues with (often) a hydrogen bond between the carbonyl oxygen of the ith main chain residue and the NH group of the i+3rd residue along the chain (O_i to NH_i+3). The subtype is defined by the Φ and Ψ angles of the middle two residues (i+1 and i+2). Often the hydrogen bond is deemed obligatory and only motives with a C_α distance between ith and i+4th residue below 7Å are considered. Each turn is assigned to one of nine classes. Helical regions are excluded from this definition and turns between beta-strands form a special class of turn known as the beta-hairpin (see later). In the following four frequent beta-turns are described.

Types I and II shown in the figure below are the most common reverse turns, the essential difference between them being the orientation of the peptide bond between residues at (i+1) and (i+2). Types I' and II' are their respected left-handed form.

beta-turns — **Beta (reverse) turn structures.** Type I and II turns (top) with their left handed counterparts (bottom) are shown. The type of a beta turn is determined by the Φ and Ψ angles of the residue i+1 and i+2. Hydrogen bonds between the Oxygen of the ith residue and the NH group of the i+3th residue are indicated with a dotted green line. Note that the turn on the top left is not forming a hydrogen bond (indicated by //) in this example. To the right the ideal dihedral angles of the i+1th (purple) and i+2rd (red) residue are shown on the ramachandran plot. The cross marks ±30º range.

Note that the (i+2) residue of the type I' and II turn lies in a region of the Ramachandran plot which is rarely occupied by non-glycine amino acids. From the diagram of I' turn it can be seen that were the (i+2) residue to have a side chain, there would be steric hindrance with the carbonyl oxygen of the preceding residue.

For further details see also the descriptions of beta truns in in PDBeMotif or PDBsum.