Conformational entropy is the entropy

Entropy

Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

 associated with the physical arrangement of a polymer

Polymer

A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...

 chain that assumes a compact or globular

Globular protein

Globular proteins, or spheroproteins are one of the two main protein classes, comprising "globe"-like proteins that are more or less soluble in aqueous solutions...

 state in solution. The concept is most commonly applied to biological macromolecule

Macromolecule

A macromolecule is a very large molecule commonly created by some form of polymerization. In biochemistry, the term is applied to the four conventional biopolymers , as well as non-polymeric molecules with large molecular mass such as macrocycles...

s such as 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 and RNA

RNA

Ribonucleic acid , or RNA, is one of the three major macromolecules that are essential for all known forms of life....

, but can also be used for polysaccharide

Polysaccharide

Polysaccharides are long carbohydrate molecules, of repeated monomer units joined together by glycosidic bonds. They range in structure from linear to highly branched. Polysaccharides are often quite heterogeneous, containing slight modifications of the repeating unit. Depending on the structure,...

s and other polymeric organic compound

Organic compound

An organic compound is any member of a large class of gaseous, liquid, or solid chemical compounds whose molecules contain carbon. For historical reasons discussed below, a few types of carbon-containing compounds such as carbides, carbonates, simple oxides of carbon, and cyanides, as well as the...

s. To calculate the conformational entropy, the possible conformations assumed by the polymer may first be discretized

Discretization

In mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers...

 into a finite number of states, usually characterized by unique combinations of certain structural parameters, each of which has been assigned an energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 level. In proteins, backbone 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 and side chain

Side chain

In organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called "main chain" or backbone. The placeholder R is often used as a generic placeholder for alkyl group side chains in chemical structure diagrams. To indicate other non-carbon...

 rotamers are commonly used as descriptors, and in RNA

RNA

Ribonucleic acid , or RNA, is one of the three major macromolecules that are essential for all known forms of life....

 the base pair

Base pair

In molecular biology and genetics, the linking between two nitrogenous bases on opposite complementary DNA or certain types of RNA strands that are connected via hydrogen bonds is called a base pair...

ing pattern is used. These characteristics are used to define the degrees of freedom

Degrees of freedom (physics and chemistry)

A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...

 (in the statistical mechanics

Statistical mechanics

Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

 sense of a possible "microstate"). The conformational entropy associated with a particular conformation is then dependent on the probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 associated with the occupancy of that state, as determined by the sum of the energies associated with the value of each parameter assumed in the state.

The entropy of heterogeneous random coil

Random coil

A random coil is a polymer conformation 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 chains in a population of macromolecules...

 or denatured

Denaturation (biochemistry)

Denaturation is a process in which proteins or nucleic acids lose their tertiary structure and secondary structure by application of some external stress or compound, such as a strong acid or base, a concentrated inorganic salt, an organic solvent , or heat...

 proteins is significantly higher than that of the folded native state

Native state

In biochemistry, the native state of a protein is its operative or functional form. While all protein molecules begin as simple unbranched chains of amino acids, once completed they assume highly specific three-dimensional shapes; that ultimate shape, known as tertiary structure, is the folded...

 tertiary structure

Tertiary structure

In biochemistry and molecular biology, the tertiary structure of a protein or any other macromolecule is its three-dimensional structure, as defined by the atomic coordinates.-Relationship to primary structure:...

. In particular, the conformational entropy of 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...

 side chain

Side chain

In organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called "main chain" or backbone. The placeholder R is often used as a generic placeholder for alkyl group side chains in chemical structure diagrams. To indicate other non-carbon...

s in a protein is thought to be a major contributor to the energetic stabilization of the denatured state and thus a barrier to protein folding

Protein folding

Protein folding is the process by which a protein structure assumes its functional shape or conformation. It is the physical process by which a polypeptide folds into its characteristic and functional three-dimensional structure from random coil....

. However, a recent study has shown that side-chain conformational entropy can stabilize native structures among alternative compact structures. The conformational entropy of RNA and proteins can be estimated; for example, empirical methods to estimate the loss of conformational entropy in a particular side chain on incorporation into a folded protein can roughly predict the effects of particular point mutation

Point mutation

A point mutation, or single base substitution, is a type of mutation that causes the replacement of a single base nucleotide with another nucleotide of the genetic material, DNA or RNA. Often the term point mutation also includes insertions or deletions of a single base pair...

s in a protein. Side-chain conformational entropies can be defined as Boltzmann sampling

Boltzmann distribution

In chemistry, physics, and mathematics, the Boltzmann distribution is a certain distribution function or probability measure for the distribution of the states of a system. It underpins the concept of the canonical ensemble, providing its underlying distribution...

 over all possible rotameric states:

where is the gas constant

Gas constant

The gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,...

 and is the probability of a residue being in rotamer .

The limited conformational range of proline

Proline

Proline is an α-amino acid, one of the twenty DNA-encoded amino acids. Its codons are CCU, CCC, CCA, and CCG. It is not an essential amino acid, which means that the human body can synthesize it. It is unique among the 20 protein-forming amino acids in that the α-amino group is secondary...

 residues lowers the conformational entropy of the denatured state and thus increases the energy difference between the denatured and native states. A correlation has been observed between the thermostability

Thermostability

Thermostability is the quality of a substance to resist irreversible change in its chemical or physical structure at a high relative temperature.Thermostable materials may be used industrially as fire retardants...

 of a protein and its proline residue content.

See also

• Configuration entropy
  Configuration entropy
  In statistical mechanics, configuration entropy is the portion of a system's entropy that is related to the position of its constituent particles rather than to their velocity or momentum. It is physically related to the number of ways of arranging all the particles of the system while maintaining...
  
  
• Folding funnel
  Folding funnel
  The folding funnel hypothesis is a specific version of the energy landscape theory of protein folding, which assumes that a protein's native state corresponds to its free energy minimum under the solution conditions usually encountered in cells...
  
  
• Molten globule
  Molten globule
  The term molten globule was first coined by A. Wada and M Ohgushi in 1983. It was first found in cytochrome c, which conserves a native-like secondary structure content but without the tightly packed protein interior, under low pH and high salt concentration...
  
  
• Loop entropy
• Protein folding
  Protein folding
  Protein folding is the process by which a protein structure assumes its functional shape or conformation. It is the physical process by which a polypeptide folds into its characteristic and functional three-dimensional structure from random coil....