chemical thermodynamics Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measuremen ...

, conformational entropy is the

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

associated with the number of conformations of a

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

. The concept is most commonly applied to biological

macromolecule A macromolecule is a very large molecule important to biophysical processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The ...

s such as proteins and

RNA Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohyd ...

, but also be used for

polysaccharide Polysaccharides (), or polycarbohydrates, are the most abundant carbohydrates found in food. They are long chain polymeric carbohydrates composed of monosaccharide units bound together by glycosidic linkages. This carbohydrate can react with w ...

s and other molecules. To calculate the conformational entropy, the possible conformations of the molecule may first be

discretized In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...

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

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat ...

. In proteins, backbone

dihedral angle A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the uni ...

s and side chain

rotamer In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds (refer to figure on single bond rotation). While any two arrangements of atoms in a molec ...

s are commonly used as parameters, and in RNA the

base pair A base pair (bp) is a fundamental unit of double-stranded nucleic acids consisting of two nucleobases bound to each other by hydrogen bonds. They form the building blocks of the DNA double helix and contribute to the folded structure of both DNA ...

ing pattern may be used. These characteristics are used to define the

degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

(in the

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

sense of a possible "microstate"). The conformational entropy associated with a particular structure or state, such as an

alpha-helix The alpha helix (α-helix) is a common motif in the secondary structure of proteins and is a right hand-helix conformation in which every backbone N−H group hydrogen bonds to the backbone C=O group of the amino acid located four residues ear ...

, a folded or an unfolded protein structure, is then dependent on the probability of the occupancy of that structure. The entropy of heterogeneous

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 ...

or denatured proteins is significantly higher than that of the

tertiary structure Protein tertiary structure is the three dimensional shape of a protein. The tertiary structure will have a single polypeptide chain "backbone" with one or more protein secondary structures, the protein domains. Amino acid side chains may inte ...

of its folded

native state In biochemistry, the native state of a protein or nucleic acid is its properly folded and/or assembled form, which is operative and functional. The native state of a biomolecule may possess all four levels of biomolecular structure, with the ...

. In particular, the conformational entropy of the

amino acid Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha am ...

side chains 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 is the physical process by which a protein chain is translated to its native three-dimensional structure, typically a "folded" conformation by which the protein becomes biologically functional. Via an expeditious and reproduc ...

.Doig AJ, Sternberg MJE. (1995). Side-chain conformational entropy in protein folding. ''Protein Science'' 4:2247-51. However, a recent study has shown that side-chain conformational entropy can stabilize native structures among alternative compact structures.Zhang J, Liu JS (2006) On Side-Chain Conformational Entropy of Proteins. PLoS Comput Biol 2(12): e168. 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 A point mutation is a genetic mutation where a single nucleotide base is changed, inserted or deleted from a DNA or RNA sequence of an organism's genome. Point mutations have a variety of effects on the downstream protein product—consequences ...

s in a protein. Side-chain conformational entropies can be defined as Boltzmann sampling over all possible rotameric states:Pickett SD, Sternberg MJ. (1993). Empirical scale of side-chain conformational entropy in protein folding. ''J Mol Biol'' 231(3):825-39. :

S = -R \sum_ p_ \ln p_

where is the

gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...

and is the probability of a residue being in rotamer . The limited conformational range of

proline Proline (symbol Pro or P) is an organic acid classed as a proteinogenic amino acid (used in the biosynthesis of proteins), although it does not contain the amino group but is rather a secondary amine. The secondary amine nitrogen is in the prot ...

residues lowers the conformational entropy of the denatured state and thus stabilizes the native states. A correlation has been observed between the

thermostability In materials science and molecular biology, thermostability is the ability of a substance to resist irreversible change in its chemical or physical structure, often by resisting decomposition or polymerization, at a high relative temperature. T ...

of a protein and its proline residue content.Watanabe K., Masuda T., Ohashi H., Mihara H. & Suzuki Y. Multiple proline substitutions cumulatively thermostabilize Bacillus cereus ATCC7064 oligo-1,6-glucosidase. Irrefragable proof supporting the proline rule. ''Eur J Biochem'' 226,277-83 (1994).

References

Protein structure Thermodynamic entropy {{thermodynamics-stub

See also

References