Helix–coil transition models are formalized techniques in

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

developed to describe conformations of linear

polymer A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their br ...

s in solution. The models are usually but not exclusively applied to

polypeptide Peptides are short chains of amino acids linked by peptide bonds. A polypeptide is a longer, continuous, unbranched peptide chain. Polypeptides that have a molecular mass of 10,000 Da or more are called proteins. Chains of fewer than twenty ...

s as a measure of the relative fraction of the molecule in an

alpha helix An alpha helix (or α-helix) is a sequence of amino acids in a protein that are twisted into a coil (a helix). The alpha helix is the most common structural arrangement in the Protein secondary structure, secondary structure of proteins. It is al ...

conformation versus

turn To turn is to rotate, either continuously like a wheel turns on its axle, or in a finite motion changing an object's orientation. Turn may also refer to: Sports and games * Turn (game), a segment of a game * Turn (poker), the fourth of five co ...

random coil In polymer chemistry, a random coil is a conformation of polymers where the monomer subunits are oriented randomly while still being bonded to adjacent units. It is not one specific shape, but a statistical distribution of shapes for all the cha ...

. The main attraction in investigating

formation is that one encounters many of the features of

protein folding Protein folding is the physical process by which a protein, after Protein biosynthesis, synthesis by a ribosome as a linear chain of Amino acid, amino acids, changes from an unstable random coil into a more ordered protein tertiary structure, t ...

but in their simplest version. Most of the helix–coil models contain parameters for the likelihood of helix

nucleation In thermodynamics, nucleation is the first step in the formation of either a new Phase (matter), thermodynamic phase or Crystal structure, structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically def ...

from a coil region, and helix propagation along the sequence once nucleated; because polypeptides are directional and have distinct

N-terminal The N-terminus (also known as the amino-terminus, NH2-terminus, N-terminal end or amine-terminus) is the start of a protein or polypeptide, referring to the free amine group (-NH2) located at the end of a polypeptide. Within a peptide, the amin ...

and

C-terminal The C-terminus (also known as the carboxyl-terminus, carboxy-terminus, C-terminal tail, carboxy tail, C-terminal end, or COOH-terminus) is the end of an amino acid chain (protein or polypeptide), terminated by a free carboxyl group (-COOH). When t ...

ends, propagation parameters may differ in each direction. The two states are * helix state: characterized by a common rotating pattern kept together by

hydrogen bond In chemistry, a hydrogen bond (H-bond) is a specific type of molecular interaction that exhibits partial covalent character and cannot be described as a purely electrostatic force. It occurs when a hydrogen (H) atom, Covalent bond, covalently b ...

s, (see

alpha-helix An alpha helix (or α-helix) is a sequence of amino acids in a protein that are twisted into a coil (a helix). The alpha helix is the most common structural arrangement in the secondary structure of proteins. It is also the most extreme type of ...

). * coil state: conglomerate of randomly ordered sequence of atoms (see

). Common transition models include the

Zimm–Bragg model In statistical mechanics, the Zimm–Bragg model is a helix-coil transition model that describes helix-coil transitions of macromolecules, usually polymer chains. Most models provide a reasonable approximation of the fractional helicity of a given ...

and the

Lifson–Roig model In polymer science, the Lifson–Roig model is a helix-coil transition model applied to the alpha helix- random coil transition of polypeptides; it is a refinement of the Zimm–Bragg model that recognizes that a polypeptide alpha helix is only s ...

, and their extensions and variations. Energy of host poly-alanine helix in aqueous solution: :

\Delta G_\text = (m-2)\Delta H_\alpha - m T \Delta S

where ''m'' is number of residues in the helix.

References

Protein structure Statistical mechanics Thermodynamic models {{statisticalmechanics-stub