A pi helix is a type of secondary structure

Secondary structure

In biochemistry and structural biology, secondary structure is the general three-dimensional form of local segments of biopolymers such as proteins and nucleic acids...

 found in protein

Protein

Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s. Although thought to be rare, π-helices are actually found in 15% of known protein structures and are believed to be an evolutionary adaptation derived by the insertion of a single amino acid into an α-helix. Because such insertions are highly destabilizing, the formation of π-helices would tend to be selected against unless it provided some functional advantage to the protein. π-helices therefore are typically found near functional sites of proteins.

Standard structure

The amino acid

Amino acid

Amino acids are molecules containing an amine group, a carboxylic acid group and a side-chain that varies between different amino acids. The key elements of an amino acid are carbon, hydrogen, oxygen, and nitrogen...

s in a standard π-helix are arranged in a right-handed helical

Helix

A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...

 structure. Each amino acid corresponds to a 87° turn in the helix (i.e., the helix has 4.1 residues per turn), and a translation of 1.15 Å

Ångström

The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....

 (=0.115 nm

Nanometre

A nanometre is a unit of length in the metric system, equal to one billionth of a metre. The name combines the SI prefix nano- with the parent unit name metre .The nanometre is often used to express dimensions on the atomic scale: the diameter...

) along the helical axis. Most importantly, the N-H

Amine

Amines are organic compounds and functional groups that contain a basic nitrogen atom with a lone pair. Amines are derivatives of ammonia, wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group. Important amines include amino acids, biogenic amines,...

 group of an amino acid forms a hydrogen bond

Hydrogen bond

A hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine, that comes from another molecule or chemical group. The hydrogen must be covalently bonded to another electronegative atom to create the bond...

 with the C=O

Carbonyl

In organic chemistry, a carbonyl group is a functional group composed of a carbon atom double-bonded to an oxygen atom: C=O. It is common to several classes of organic compounds, as part of many larger functional groups....

 group of the amino acid five residues earlier; this repeated i+5→i hydrogen bonding defines a π-helix. Similar structures include the 3₁₀ helix (i+3→i hydrogen bonding) and the α-helix

Alpha helix

A common motif in the secondary structure of proteins, the alpha helix is a right-handed coiled or spiral conformation, in which every backbone N-H group donates a hydrogen bond to the backbone C=O group of the amino acid four residues earlier...

 (i+4→i hydrogen bonding).

The majority of π-helices are only 7 residues in length and do not adopt regularly repeating (φ, ψ) dihedral angle

Dihedral angle

In geometry, a dihedral or torsion angle is the angle between two planes.The dihedral angle of two planes can be seen by looking at the planes "edge on", i.e., along their line of intersection...

s throughout the entire structure like that of α-helices or ß-sheets. Because of this, textbooks that provide single dihedral values for all residues in the π-helix are misleading. Some generalizations can be made, however. When the first and last residue pairs are excluded, dihedral angles exist such that the ψ dihedral angle

Dihedral angle

In geometry, a dihedral or torsion angle is the angle between two planes.The dihedral angle of two planes can be seen by looking at the planes "edge on", i.e., along their line of intersection...

 of one residue and the φ dihedral angle of the next residue sum to roughly -125°. The first and last residue pairs sum to -95° and -105°, respectively. For comparison, the sum of the dihedral angles for a 3₁₀ helix is roughly -75°, whereas that for the α-helix is roughly -105°. Proline is often seen immediately following the end of π-helices. The general formula for the rotation angle Ω per residue of any polypeptide helix with trans isomers is given by the equation

Left-handed structure

In principle, a left-handed version of the π-helix is possible by reversing the sign of the (φ, ψ) dihedral angle

Dihedral angle

In geometry, a dihedral or torsion angle is the angle between two planes.The dihedral angle of two planes can be seen by looking at the planes "edge on", i.e., along their line of intersection...

s to (55°, 70°). This pseudo-"mirror-image" helix has roughly the same number of residues per turn (4.1) and helical pitch (1.5 angstroms or 150 picometers). It is not a true mirror image, because the amino-acid

Amino acid

Amino acids are molecules containing an amine group, a carboxylic acid group and a side-chain that varies between different amino acids. The key elements of an amino acid are carbon, hydrogen, oxygen, and nitrogen...

 residues still have a left-handed chirality

Chirality (chemistry)

A chiral molecule is a type of molecule that lacks an internal plane of symmetry and thus has a non-superimposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom....

. A long left-handed π-helix is unlikely to be observed in proteins because, among the naturally occurring amino acids, only glycine

Glycine

Glycine is an organic compound with the formula NH2CH2COOH. Having a hydrogen substituent as its 'side chain', glycine is the smallest of the 20 amino acids commonly found in proteins. Its codons are GGU, GGC, GGA, GGG cf. the genetic code.Glycine is a colourless, sweet-tasting crystalline solid...

is likely to adopt positive φ dihedral angles such as 55°.