1.0 Helices

Learning Outcomes

• Describe the principal geometry of alpha helices in terms of n, d, r, and p.
• Describe the main structural characteristics of alpha helices
• Use molecular visualisation tools to explore the geometry, and structure, of alpha helices

Helices are repetitive secondary structures because their backbone φ (phi) and ψ (psi) angles are repeated geometrically along the structure. In an 'ideal' right-handed, alpha helix, φ (phi) = -57 and ψ (psi) = -47. Helices can be described by five parameters as shown below and in Table 1.1 and Figure 1.1:

d= distance traveled per repeating unit (parallel to the helix axis)

n=number of 'repeating units' (ie residues) per turn of the helix

p=pitch distance between successive points between one complete turn of the helix

r=radius of helix

angle = the angle of rotation of each residue within the helix - this is 100 degrees. (Note: the angle is not shown in Table 1.1 or Figure 1.1 but shown in Figure 1.6)

Table 1.1 Parameters of helix structures found in Proteins

Secondary Structure	Residues per turn n	Rise per residue d (Å)	Radius of helix r (Å)
α-helix	+3.6	1.5	2.3
3.10 helix	+3.0	2.0	1.9
left handed α-helix	-3.6	1.5	2.3
π-helix	+4.3	1.1	2.8
collagen helix	-3.3	2.9	1.6
Note that plus sign indicates a right-handed helix and negative sign a left-handed helix. Values rounded to two significant figures

Helices can be 'right' or 'left' handed as shown in Figure 1.2. If the helix spirals in the same direction that the four fingers of the right hand are pointing then it is a right handed helix. Traditionally, helices are named according to the number of residues per turn of the helix and the number of atoms contained in a ring defined by the hydrogen bond Figure 1.3. Consequently, the α,3.10, and π helices are 3.6₁₃, 3₁₀, and 4.4₁₆, respectively. However, there are ambiguities in this naming convention because 3.6₁₃ and 3.7₁₃ are both alpha helices.

The three types of 'ideal' helices are shown in the space-filled model of a twelve residue helix of Figure 1.4. You can see that as the number of residues per turn increases from 3.10 (3₁₀ helix) to 3.6 (α-helix) and then to 4.4 (π-helix) the structures become more compact and hence less stable due to increased steric hindrance between the atoms. The spatial arrangement of the atoms in these helices can also be seen in the cylindrical plot shown in Figure 1.5 where the path of the alpha carbon atoms is traced along the helix.

Another way of representing the helix is as a 'helix wheel' shown in Figure 1.6 and shows a diagram of the turns in a helix where a side chain within the helix is represented by the apex of the polygons of the plot. This representation is useful in showing the amphilicity of the helix.

To help you understand the structure of a helix Figure 1.10 is a diagram you can cut out and twist into a helix using your knowledge of helix structure. Also provided are Figure 1.11 and Figure 1.12 which are pdb files of a polyalanine alpha helix and a myoglobin helix respectively which you can use to help you understand helix structure.

Summary of the characteristics of the three types of helix

1.1 a-helix characteristics

• First described by Linus Pauling about 1951 - based on his calculations of peptide bond lengths and torsional angles. His theory was later given experimental support from X-ray crystallography of haemoglobin crystals (performed by Max Perutz) and myoglobin (performed by John Kendrew).

• most abundant helical conformations in proteins and accounts for 32 to 38% of all residues

• A a-helix is formed from one region of the polypeptide when a stretch of consecutive residues have φ and ψ (psi) angles of about -57 and -47 respectively (Figure 1.7).

• residues per turn ie. n= 3.6, p= 5.4 Å, and d=1.5 Å and each residue has a rotation of about 100 degrees

• the radius of the helix allows for favourable van der Waals interactions across the helix and there are no 'holes' within the helix

• hydrogen bonds between C=O of residue n and NH of residue n+4

• the carbonyl oxygens point toward the C-terminal end of the helix and the amide hydrogens point toward the N-terminal end of the helix

• the peptide planes are roughly parallel with axis of helix

• varies in length from 4 to over 40 residues - average about 10 residues

• side chains of amino acids comprising the helix tend to point outward from the helix (Figure 1.8) and are staggered to reduce steric interactions

• most right handed but do have left handed helix

• most helix are distorted from the 'ideal' model (ie. phi -57 and psi -47) due to various interactions (see below)

• electric dipole transmitted along axis of the helix through the action of hydrogen bonds all acting in the same direction. This usually leaves a slight positive ( δ⁺ ) charge at the amino end of the helix and a slight negative charge ( δ^- ) at the carboxyl end of the helix (Figure 1.9). Consequently, we usually also find negatively charged residues at the amino end and positively charged residues at the carboxyl end to counteract the dipole.

• the helix can exhibit amphiphillic character ie. they have a hydrophobic and a hydrophilic face (Figure 1.6). Consequently, many helices are found on the surface of globular proteins and project their hydrophobic face towards the core and the hydrophilic face towards the solvent.

 1.11 Factors affecting the stability and orientation of the helix:

• electrostatic repulsion and attraction between helix atoms

• side chain bulk (destabilise)

• interactions between residue side chains spaced 3-4 residues apart (stabilise or destabilise depending upon the side chains)

• presence of proline introduces a 'kink' to the helix and breaks hydrogen bonds (destabilise - although this depends upon preceding residues. Proline can also help form a helix)

• interaction between residues at the end of the helix and the dipole (stabilise or destabilise depending upon the residues)

• interaction of carbonyl group (C=O) with solvent tends to bend the helix slightly along its longitudinal axis (stabilise)

• interaction with other secondary structure elements within protein (stabilise - especially when in four-helix bundles seen later)

• helices can be 'capped' either at the N-terminal, the C-terminal, or both ends of the helix by residues which form extra hydrogen bonds to both main chain (polypeptide backbone) and sidechain atoms. This has a tendency to stabilise the helix.

1.2 Other helices

The 3.10 helix and the pi-helix are rare helix structures within proteins (eg. less than 4% of the residues within a protein are involved in forming a 3.10 helix). However, the 3.10 helix is the fourth most common type of secondary structure element after α-helices, β-strands, and turns. We will not go into detail here, but you should be aware of them. In particular, you should notice that 3.10 helices are usually only comprised of three to five residues and that as the number of residues per turn increases from 3 (3.10 helix) to 3.6 (α-helix) and then to 4.4 (π-helix) the structures become more compact and hence less stable due to increased steric hindrance between the atoms.

Questions to review Learning Outcomes

1. Determine the formula that relates the helix parameters: n, d, and p
2. The φ and ψ angles given for a α helix are so called 'ideal' angles. Why is this? What do you think these angles represent? Hint: Take a look at the Ramachandran plot.
3. One way of analysing a helix is by a cylindrical plot of the α-carbon atoms (Figure 1.5 ). Calculate the height and length of the rectangle given that the plot is of one complete turn of a α-helix. Calculate the length, and angle, of the diagonal. What do you notice about your calculations? What does the angle of the diagonal represent?
4. The photoreactive protein (2PHY) has an unusual α-helix in its structure. Use your molecular visualisation skills to discover why it is unusual and suggest at least one way the protein seems to be able to stabilise this secondary structure.