Pi helix

A pi helix (or π-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 organic compounds made of amino acids arranged in a linear chain and folded into a globular form. The amino acids in a polymer chain are joined together by the peptide bonds between the carboxyl and amino groups of adjacent amino acid residues...

s. This structure is particularly common in membrane proteins.

Standard structure

The amino acid

Amino acid

Amino acids are molecules containing an amine group, a carboxylic acid group and one of the twenty R-groups. These molecules are particularly important in biochemistry, where this term refers to alpha-amino acids with the general formula H₂NCHRCOOH, where R is an organic substituent...

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

Helix

A helix is a special kind of space curve, i.e. a smooth curve in three-space. As a mental image of a helix one may take the spring...

 structure. Each amino acid corresponds to a 87° turn in the helix (i.e., the helix has 4.4 residues per turn), and a translation of 1.15 Å

Ångström

The ångström or angstrom is an internationally recognized unit of length equal to 0.1 nanometre or 1 metres. It is named after Anders Jonas Ångström...

 (=0.115 nm

Nanometre

A nanometre is a unit of length in the metric system, equal to one billionth of a meter....

) 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 Amines are derivatives of ammonia, wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group.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, like nitrogen, oxygen or fluorine . 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.The term carbonyl can also refer to carbon monoxide as a ligand in an inorganic or organometallic complex In organic chemistry, a carbonyl group is a functional group...

 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 (i+4→i hydrogen bonding).

Residues in π-helices typically adopt (φ, ψ) dihedral angle

Dihedral angle

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

s near (-55°, -70°). More generally, they adopt dihedral angles such that the ψ dihedral angle

Dihedral angle

In geometry, the angle between two planes is called their dihedral or torsion angle.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°. For comparison, the sum of the dihedral angles for a 3₁₀ helix is roughly -75°, whereas that for the α-helix is roughly -105°. 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, the angle between two planes is called their dihedral or torsion angle.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 one of the twenty R-groups. These molecules are particularly important in biochemistry, where this term refers to alpha-amino acids with the general formula H₂NCHRCOOH, where R is an organic substituent...

 residues still have a left-handed chirality

Chirality (chemistry)

The term chiral is used to describe an object that is non-superposable on its mirror image. Achiral objects are objects that are identical to their mirror image....

. 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. With only a hydrogen atom as its side chain, glycine is the smallest of the 20 amino acids commonly found in proteins....

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