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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. Two torsion angles phi (N, Calpha, C, N) and psi (Calpha,C,N,Calpha) are on either side of the C alpha atom while omega (O,C,N,H) describes the angle for the actual peptide bond.

Peptide torsion angles and indication of resonance in the peptide bond
Peptide torsion angles. A chain of two amino acids is shown with the three torsion angles phi, psi and omega indicated. While both the phi and psi angle have a high rotational freedom, the omega angle is locked in either the trans-state (180 degrees) or more rarely in the cis-state (10 degrees). The resonance of the amide bond is indicated in light blue.

The planarity of the peptide bond restricts the omega torsion angle to 180 degrees (trans state) in nearly all of the main chain peptide bonds. In rare cases omega = 10 degrees for a cis peptide bond which usually involves proline.

The partial double bond character of the peptide (amide) bond, caused by the delocalisation of the lone pair of the nitrogen into the peptide bond, causing planarity in the peptide group. The resonance in the peptide bond (N-C=O <-> N+=C-O-) is highlighted in 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 omega angles are restricted, the polypeptide main chain exhibits considerable freedom to rotate around the N-Ca (phi torsion) and Ca-C (psi torsion) bonds. This fact is employed in the ramachandran plot, where the phi / psi space is visualized. GN Ramachandran (Ramachandran, Ramakrishnan, and Sasisekharan 1963) used computer models of small polypeptides to systematically sample the phi/psi 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. identified several key secondary structures. 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 phi and psi 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 protein structures known newer iteration of the Ramachandran plot are based on distributions found in the structures. The Ramachandran plots represented here are made with MolProbity (Chen VB et al.) via the Phenix suite (Adams PD et al.)

The favoured part of the plot encloses 98% of the good data, while the allowed part encloses 99.95% of the good data.

General Ramachandran Plot from MolProbity, Glycines and Prolines are not included in this plot.
General Ramachandran plot from MolProbity. For clarity the thickness of the line enclosing the favoured region was increased.

In the original calculations of Ramachandran GN et al. the disallowed region was based on the observation of sterical clashes between the sidechain of one amino acid with the backbone of the succeeding amino acid. An exception to this is glycine since it lacks the sidechain responsible for the clash. On the other hand proline's phi angle is locked around -60º.

Ramachandran Plot from MolProbity for Glycines.Ramachandran Plot from MolProbity for Prolines in trans conformation.
Ramachandran plot from MolProbity for Glycine and Proline in trans state.

1.3 The alpha-helix.

1.3.1 Development of an alpha-helix structure model.

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'.

Side-view of an alpha helix.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 Cbeta carbon of the protein is shown.

Cartoon view of human adenosine A1 receptor A1AR-bRIL, pdb entry: 5UENRamachandran 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.

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:

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. Oi to Ni+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 stile and for clarity only the backbone and Cbeta atom is shown. 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 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 negative phi and psi 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.

Imagining two strands parallel to the stand shown above, either in the plane with the strand (top strand), or one above the plane of the screen and one behind (bottom strand), 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 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 Cbeta 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 Cbeta 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 (Oi to NHi+3). The subtype is defined by the phi and psi angles of the middle two residues (i+1 and i+2). Often the hydrogen bond is deemed obligatory and only motives with a Calpha 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 (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 phi and psi 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.