Conformational entropy

Conformational entropy is the entropy associated with the physical arrangement of a polymer chain that assumes a compact or globular state in solution. The concept is most commonly applied to biological macromolecules such as proteins and RNA, but can also be used for polysaccharides and other polymeric organic compounds. To calculate the conformational entropy, the possible conformations assumed by the polymer must first be discretized into a finite number of states, usually characterized by unique combinations of a relatively small number of parameters, each of which has been assigned an energy. In proteins, backbone dihedral angles and side chain rotamers are commonly used as descriptors, and in RNA the base pairing pattern is used. These characteristics are used to determine the degrees of freedom (in the statistical mechanics sense of a possible "microstate"). The conformational entropy associated with a particular conformation is then the probability 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.

Explicit descriptions of the conformational entropy are sometimes used in RNA structure prediction, but are difficult to calculate for proteins due to their large variety of possible states. Nevertheless, the concept of conformational entropy is often used in an informal sense to capture the high entropy associated with heterogeneous protein random coil or denatured states as compared to the relatively homogeneous native state tertiary structure. In particular, the conformational entropy of the amino acid 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. Empirical methods to estimate the loss of conformational entropy in a particular side chain on incorporation into a folded protein have been developed and can roughly predict the effects of particular point mutations in a protein. Side-chain conformational entropies can be defined as Boltzmann sampling over all possible rotameric states:

$S=-R\Sigma _{i}p_{i}ln(p_{i})$

where $R$ is the gas constant and $p_{i}$ is the probability a residue being in rotamer $i$.

The limited conformational range of proline 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 of a protein and its proline residue content.

See also

• Folding funnel
• Molten globule
• Protein folding