Introduction

Proteins are the "worker" molecules of a cell. Their correct functioning and interaction with other molecules in the cell is crucial for many aspects of life. Proteins are involved in transport (hemoglobin: oxygen), storage (myoglobin in the muscle: oxygen), movement (dynein, actin), recognition (insulin receptors: protein kinase activation through binding of the hormone insulin), signal transduction (epidermal growth factor: cell growth), protection (antibodies), energy storage (glycogenin: glycogen), metabolism (F1-ATPase: ATP generation) and structure (keratin: skin).

The goal of this course is to revisit basic principles of protein structures and familiarize yourself with sources of experimental and theoretical protein structure models.

1 Backbone conformation and secondary structure

1.1 Peptide Torsion Angles

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

The planarity of the peptide bond is restricted to 180 ° in nearly all of the main chain peptide bonds. In rare cases a deviation of 10 °  for a cis peptide bond is observed, that usually involves Proline.

1.2 The Ramachandran Plot

In a polypeptide the main chain N-Cα and Cα-C bonds are relatively free to rotate. These rotations are represented by the torsion angles phi (Φ: C-N-Cα-C) and psi (ψ: N-Cα-C-N), respectively.

G.N. Ramachandran used computer models of small polypeptides to systematically vary torsional angles 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. Angles, which cause spheres to collide correspond to sterically disallowed conformations of the polypeptide backbone.

In the diagram above the dark blue and black areas correspond to conformations where atoms in the polypeptide come closer than the sum of their van der Waals radii. These regions are sterically disallowed for all amino acids except Glycine, which is unique in that it lacks a side chain. The red/yellow regions correspond to conformations where there are no steric clashes, i.e. these are the allowed regions namely the α-helical and β-sheet conformations. The green areas show the allowed regions if slightly shorter van der Waals radii are used in the calculation, i.e. the atoms are allowed to come a little closer together. This brings out an additional region which corresponds to the left-handed α-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 stabilizes this otherwise unfavourable conformation. The 3₁₀ helix occurs close to the upper right of the α-helical region and is on the edge of the allowed region indicating lower stability.

Disallowed regions generally involve steric hindrance between the side chain CH2 group 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.

Below is a Ramachandran plot of a protein containing almost exclusively β-strands (yellow dots) and only one helix (red dots). Note how few residues are out of the allowed regions. Note also that they are almost all Glycines (depicted with a little square instead of a cross).

Observe the effect of minor phi  (Φ) and psi (ψ)  angle changes:

1.2 The α-helix.

1.2.1 Development of an α-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 α-keratin fibre diffraction data. The most simple and elegant arrangement is a right-handed spiral conformation known as the 'α-helix'.

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.

1.2.2 Properties of the α-helix.

The structure repeats itself every 5.4 Å along the helix axis, i.e. we say that the α-helix has a pitch of 5.4 Å. α-helices have 3.6 amino acid residues per turn, i.e. 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 Å, i.e. the α-helix has a rise per residue of 1.5 Å.

1. 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.
2. 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.

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

1.2.3 Distortions of α-helices.

The majority of α-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 ° 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.
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 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.

3₁₀-Helices.

Strictly, these form a distinct class of helix but they are always short and frequently occur at the termini of regular α-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 α-helix is a 3.6₁₃-helix. The dipoles of the 3₁₀-helix are not so well aligned as in the α-helix, i.e. it is a less stable structure and side chain packing is less favourable.

1.3 The β-sheet.

1.3.1 The β-sheet structure.

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

In a β-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 β-sheet are between different segments of polypeptide. This contrasts with the α-helix where all hydrogen bonds involve the same element of secondary structure. The R-groups (side chains) of neighboring residues in a β-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 β-sheet arises. Note that peptide groups of adjacent residues point in opposite directions whereas with a-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 β-strand a 7 Å pitch. This compares with the α-helix where the axial distance between adjacent residues is only 1.5 Å. Clearly, polypeptides in the β-conformation are far more extended than those in the α-helical conformation.

1.3.2 Parallel, anti-parallel and mixed β-sheets.

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

Below is a diagram of a three-stranded anti-parallel β-sheet. It emphasizes the highly regular pattern of hydrogen bonds between the main chain NH and CO groups of the constituent strands.

In the classical Pauling-Corey model the parallel β-sheet is somewhat more distorted and consequently exhibit weaker hydrogen bonds between the strands.

β-sheets are very common in globular proteins and most contain less than six strands. The width of a six-stranded β-sheet is approximately 25 Å. No preference for parallel or anti-parallel β-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 anti-parallel, but mixed sheets do occur.

The Pauling-Corey model of the β-sheet is planar. However, most β-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 ° per amino acid in a right-handed sense.

Parallel sheets are less twisted than anti-parallel and are always buried. In contrast, anti-parallel sheets can withstand greater distortions (twisting and b-bulges) and greater exposure to solvent. This implies that anti-parallel 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).

The left-handed twist of beta sheets amounts to 25º between each neighboring strands.

1.4 Reverse turns

A reverse turn is region of the polypeptide having a hydrogen bond from one main chain carbonyl oxygen to the main chain N-H group 3 residues along the chain (i.e. O_i to N_i+3). Helical regions are excluded from this definition and turns between β-strands form a special class of turn known as the β-hairpin (see later). Reverse turns are very abundant in globular proteins and generally occur at the surface of the molecule. It has been suggested that turn regions act as nucleation centres during protein folding.

Reverse turns are divided into classes based on the Φ and Ψ angles of the residues at positions i+1 and i+2. 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).

The torsion angles for the residues (i+1) and (i+2) in the two types of turn lie in distinct regions of the Ramachandran plot.

Note that the (i+2) residue of the type II turn lies in a region of the Ramachandran plot which can only be occupied by Glycine. From the diagram of this 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. Hence, the (i+2) residue of type II reverse turns is nearly always Glycine.